For food to be כָּשֵׁר kosher, it must be in accordance with הֲלָכָה halakah (Jewish law). הֲלָכָה Halakha has a comprehensive set of dietary laws collectively called the כַּשְׁרוּת kashrut.
The Written תּוֹרָה Torah, particularly Leviticus and Deuteronomy, form the כַּשְׁרוּת kashrut's core. The biblical laws are expounded in the תַּלְמוּד Talmud and מדרש Midrash, collectively known as the Oral Torah because they are our records of how the Written תּוֹרָה Torah was understood and interpreted.
Particularly, the Oral Torah creates a gezeirah (fence around the תורה שבכתב Torah) of extra measures and precautions to avoid accidental violations of rules set down in the תּוֹרָה Torah. Additional dietary laws are followed during certain holidays. Also, food from Israel faces further scrutiny.
טרײף treif is a Yiddish word referring to any food that is not כָּשֵׁר kosher, whether a forbidden species, disallowed death or impermissible mixture.
The most lackadaisical Jew may only avoid pork and shy away from mixing meat and dairy. However, full כַּשְׁרוּת kashrut is much richer than just that, and there is an array of traditions held in order to enforce כַּשְׁרוּת kashrut.
Much of כַּשְׁרוּת kashrut concerns itself with brutality and respect for life (animal vs human nature), and cleanliness.
Beastly animals are forbidden, only the timid, vegetarian animals may be eaten. Filter-feeders that uptake feces, land animals that feast on feces, are all forbidden with broad, sweeping definitions that elegantly permit only those animals that fit in an intuitive, gentle framework.
כָּשֵׁר Kosher food must not have been involved in idolatry.
It is forbidden to consume anything that was used in a ceremony dedicated to an alien deity. For instance, food that has been sacrificed to an idol is not ritually clean. An extension of this rule applies to wine. Since wine was historically used in idolatrous libations, many Conservative and especially Orthodox Jews entirely forbid wine from non-Jewish makers.
Similarly, it is believed that pork is forbidden because Egyptian priests ate it almost exclusively.
כָּשֵׁר Kosher food may not have died of natural causes.
Exodus states that it is forbidden to eat meat from animals torn by beasts. In fact, if an animal is not slaughtered by prescribed methods, it may not be eaten. Deuteronomy corroborates this and totally prohibits consuming, gifting nor selling anything that died of any natural cause.
And if any animal which you may eat dies, whoever touches its carcass shall be unclean until the evening, and whoever eats of its carcass shall wash his clothes and be unclean until the evening. And whoever carries the carcass shall wash his clothes and be unclean until the evening. Leviticus 11:39-40
Regarding sea animals, only fish are permitted.
Leviticus and Deuteronomy allow water-dwelling animals only if they have both fins and scales. This forbids all the invertebrates of seas, rivers and lakes, which includes crustaceans and mollusks: clam, lobster, crab, squid, octopus and all other filter-feeders are not כָּשֵׁר kosher. כַּשְׁרוּת Kashrut forbids eel, the only animal with scales but not fins.
Since they lack scales, whale, dolphin, catfish and sturgeon (thereby, caviar too) are not כָּשֵׁר kosher. And yes, if considered water animals, platypus and beavers are not כָּשֵׁר kosher (and if considered land animals, they are banned because they are quadrupeds that have paws, and also because they go on their bellies).
Of all the marine animals, you may eat whatever has both fins and scales. You may not, however, eat marine animals that do not have both fins and scales. They are ceremonially unclean for you. Deuteronomy 14:9-10
Technically, all winged creatures are allowed except for those expressly forbidden in Leviticus' list of detestable birds.
Though the written תּוֹרָה Torah technically only forbids a limited list of winged animals, an exegesis reveals some groupings which are avoided in the הֲלָכָה halakah. Many birds of prey and scavengers are forbidden; these typically eat much carrion, or prey on living animals. Also, many birds are forbidden that dwell on water and eat fish; their diet also often includes unclean water creatures.
Thus, only birds that are primarily land-dwelling and vegetarian are permitted. Of those, however, ostriches (and by tradition, related species such as the emu) are not permitted.
These you shall detest among the birds; they shall not be eaten; they are detestable: the eagle, the bearded vulture, the black vulture, the kite, the falcon of any kind, every raven of any kind, the ostrich, the nighthawk, the sea gull, the hawk of any kind, the little owl, the cormorant, the short-eared owl, the barn owl, the tawny owl, the carrion vulture, the stork, the heron of any kind, the hoopoe, and the bat. Lev. 11:13-19
כָּל-צִפּוֹר טְהֹרָה, תֹּאכֵלוּ.
[All - a bird ritually pure (taharah) eat.] Of all clean birds ye may eat.
וְזֶה, אֲשֶׁר לֹא-תֹאכְלוּ מֵהֶם: הַנֶּשֶׁר וְהַפֶּרֶס, וְהָעָזְנִיָּה
[And, which do not - not eat them: the eagle/vulture and the prize, and Eurasian] But these are they of which ye shall not eat: the great vulture, and the bearded vulture, and the ospray;
וְהָרָאָה, וְאֶת-הָאַיָּה, וְהַדַּיָּה, לְמִינָהּ
[And showed, and - the falcon, and heidia, after their kind] and the glede, and the falcon, and the kite after its kinds;
וְאֵת כָּל-עֹרֵב, לְמִינוֹ
[And all - Arab gender] and every raven after its kinds;
וְאֵת בַּת הַיַּעֲנָה, וְאֶת-הַתַּחְמָס וְאֶת-הַשָּׁחַף; וְאֶת-הַנֵּץ, לְמִינֵהוּ
[And the ostrich, and the - whippowill and - seagull; and - hawk after its kind] and the ostrich, and the night-hawk, and the sea-mew, and the hawk after its kinds;
אֶת-הַכּוֹס וְאֶת-הַיַּנְשׁוּף, וְהַתִּנְשָׁמֶת
[The - cup and - the owl, and barn owl] the little owl, and the great owl, and the horned owl;
וְהַקָּאָת וְאֶת-הָרָחָמָה, וְאֶת-הַשָּׁלָךְ
[And vomiting and - her womb, and - discard] and the pelican, and the carrion-vulture, and the cormorant;
וְהַחֲסִידָה, וְהָאֲנָפָה לְמִינָהּ; וְהַדּוּכִיפַת, וְהָעֲטַלֵּף
[And the stork, and the heron after her kind, and the hoopoe, and the bat] and the stork, and the heron after its kinds, and the hoopoe, and the bat.
וְכֹל שֶׁרֶץ הָעוֹף, טָמֵא הוּא לָכֶם: לֹא, יֵאָכֵלוּ
[And all swarming/running/creeping/varmint bird, he is unclean to you: No, eating] And all winged swarming things are unclean unto you; they shall not be eaten.
כָּל-עוֹף טָהוֹר, תֹּאכֵלוּ
[All - ritually pure (tahor) bird, you may eat] Of all clean winged things ye may eat. Deuteronomy 14:11-20
Leviticus 11 and Deuteronomy 14 begin by explicitly permitting animals with cloven hoofs and which re-digest their food.
Cloven hoofs are visually apparent: what are in fact two separate toes appear like a bifurfated hoof, a cloven hoof. Animals that re-digest their foods include the ruminants (chewing the cud), a group of vegetarian creatures that chew, swallow, partially digest, then regurgitate back into their mouth for further chewing. Also, some animals (namely rodents) re-ingest their feces.
A land animal is clean if it has both qualities, but unclean if it only has one of those qualities. Leviticus 11:3-8 and Deuteronomy 14:4-8 explicitly list the camel, hare, hyrax and pig as unclean animals for this reason (though the camel actually has two toes with pads, not hoofs). Cattle, goat, deer and other cloven-hoofed, ruminating herbivores are permitted.
These are the animals you may eat: the ox, the sheep, the goat, the deer, the gazelle, the roe deer, the wild goat, the addax, the antelope, and the mountain sheep. You may eat any animal that has completely split hooves and chews the cud, but if the animal doesn't have both, it may not be eaten. So you may not eat the camel, the hare, or the hyrax. They chew the cud but do not have split hooves, so they are ceremonially unclean for you. And you may not eat the pig. It has split hooves but does not chew the cud, so it is ceremonially unclean for you. You may not eat the meat of these animals or even touch their carcasses. Deuteronomy 14:4-8 (also see Leviticus 11:3-8)
This general rule does not expressly forbid land animals that are not cloven-hoofed and ruminant. However, Leviticus goes on to forbid effectively all other land animals.
Beyond cloven-hoofed ruminants, Deuteronomy does not discuss any other animals as being כָּשֵׁר kosher or not. Only Leviticus delves further (and quite expansively) into land animals. Leviticus lays out several categories, all of which are forbidden: four-legged animals that go on their paws; animals that go on their bellies; animals with many feet; and animals with the trait רמש remes, referring to small varmin such as mice. רמש Remes is translated as swarm, creep, scurry, crawl or teem (creeping things that creep on the earth and swarming things that swarm on the ground are the same, just alternate translations).
Considering the nature of these groups, it is clear that they are not gentle vegetarians. These are carnivores, omnivores, scavengers, coprophages; animals that prey, scurry, bite, sting, slither. The meaning of swarm may seem ambiguous -- but consider the way that scavengers and coprophages descend on their meals, and it is clear that swarm is uniquely a trait of unclean animals. Creeping things that creep on the earth then goes on to forbid many rodents.
And all that walk on their paws, among the animals that go on all fours, are unclean to you. ... And these are unclean to you among the swarming things that swarm on the ground: the mole rat, the mouse, the great lizard of any kind, the gecko, the monitor lizard, the lizard, the sand lizard, and the chameleon. These are unclean to you among all that swarm. .... Every swarming thing that swarms on the ground is detestable; it shall not be eaten. Whatever goes on its belly, and whatever goes on all fours, or whatever has many feet, any swarming thing that swarms on the ground, you shall not eat, for they are detestable. You shall not make yourselves detestable with any swarming thing that swarms, and you shall not defile yourselves with them, and become unclean through them. Leviticus 11:27,29-30,41-43
All rodents are not כָּשֵׁר kosher because they have four legs and paws, and also because they dwell on the ground (thus the platypus is also not כָּשֵׁר kosher).
Other pawed quadrupeds are canines, felines and indeed all carnivorous mammals (besides whales and dolphins, which are forbidden for lacking scales). All reptiles (snakes, lizards, turtles, crocodiles) go on their bellies and are thus not כָּשֵׁר kosher. The same applies to amphibians (salamanders, newts, frogs, etc).
Indeed, consider that many reptiles and amphibians scavenge and eat bugs, two practices which are unclean.
No bugs are כָּשֵׁר kosher except certain species of locust.
Any bug with wings that walks on the ground is unclean, except those that hop on the ground: locusts, crickets and grasshoppers.
Deuteronomy describes forbidden bugs as impure, while Leviticus deplores them as filth.
וְכֹל שֶׁרֶץ הָעוֹף, טָמֵא הוּא לָכֶם: לֹא, יֵאָכֵלוּ
[And all swarming/running/creeping/varmint bird, he is unclean to you: No, eating]
And all winged swarming things are unclean unto you; they shall not be eaten. Deuteronomy 14:19
You must not eat winged insects that walk along the ground; they are detestable to you. You may, however, eat winged insects that walk along the ground and have jointed legs so they can jump. The insects you are permitted to eat include all kinds of locusts, bald locusts, crickets, and grasshoppers. All other winged insects that walk along the ground are detestable to you. Leviticus 11:20-23
Those animals not described in Leviticus and Deuteronomy are by tradition not permitted.
Primates (monkeys, gorillas, chimpanzees), marsupials (koalas, kangaroos), equids (horses) are not defined in the כַּשְׁרוּת kashrut passages of Leviticus nor Deuteronomy, but tradition maintains that they are not כָּשֵׁר kosher. Monotremes (egg-laying mammals such as the platypus) are not explicitly discussed but as they have four legs, paws and go on their bellies they are not כָּשֵׁר kosher.
Many Jews will not eat any animal that is not part of a mesorah (tradition), even if otherwise כָּשֵׁר kosher. Examples include zebu and bison (which were not available at the time). Also, swans are allowed by כַּשְׁרוּת kashrut but not included in tradition.
Meat and Dairy
Deuteronomy and Exodus forbid boiling a kid in its mother's milk. In practice, this rule is greatly expanded.
The word בישול bishul is translated as boiling or seething, but is thought to mean cooking in general. The word גדי g'di means young goat, but it a short (likely more general) form of the usual word for a young goat (g'di izim). Thus, the written תּוֹרָה Torah is believed to forbid cooking in milk any young animal that suckles. This is thought to be out of respect for the mother and her kid's life.
When I was a youth I was vaguely aware of the ban on mixing meat and dairy. I considered it arcane. But after reading the text and its exegesis, I imagined milking a cow, then slaughtering her calf and cooking it in its mother's milk. The idea was revolting. My thought was, "Well, if you put it that way."
לֹא-תְבַשֵּׁל גְּדִי, בַּחֲלֵב
[No - boil a kid, in milk] Exodus 34:26
לֹא-תְבַשֵּׁל גְּדִי, בַּחֲלֵב אִמּוֹ
[No - boil a kid, his mother's milk] Exodus 23:19, Deuteronomy 14:21
This rule has been expanded by many Jews to forbid cooking any meat in dairy, and even entirely separating the two.
The rule forbidding any contact between any meat (besides seafood) and dairy is actually a gezeirah. The reasoning is that, for example, chicken and mutton could be easily confused; but seafood is visually and olfactorily distinct and thus cannot be confused. This gezeirah is not followed by all Jews, namely the Karaite, Ethiopian and some Persian Jewry; not just fish, but poultry also is considered pareve (neutral) by these groups.
Many more rules have been edified to avoid mixing, whether by residue on wares, accidental ingestion due to proximity or any other possibility. At their fullest, these rules include separate sets of dishes and utensils for meat and dairy, and even separate cooking spaces.
Pareve comes from the Yiddish word פאַרעוו parev, meaning neutral. Pareve food may be mixed with either meat or dairy.
There are thus three groupings into which foods may fall: meat (Hebrew בשרי basari; Yiddish פֿליישיק fleishik); dairy (Hebrew חלבי halavi; Yiddish מילכיק milkshik); and pareve (Yiddish פאַרעוו parev). Meat and dairy may not be mixed, but pareve foods are neutral. Pareve foods may be combined either either meat or dairy.
All vegetable materials are pareve. Also, fish is pareve and can be cooked with other meats or dairy. However, their is dispute over poultry. Some Jewry consider poultry to be pareve, as poultry does not suckle. But more restrictive (indeed, most) interpretations deem poultry not pareve and thus non-mixable with dairy.
שחיטה Shechita (Slaughter)
שחיטה Shechita is the method of slaughter prescribed by the כַּשְׁרוּת kashrut, necessary for an animal to be כָּשֵׁר kosher.
Deuteronomy 12:21 dictates that sheep and cattle are to be slaughtered as commanded by G_d when offered as a sacrifice. In practice, this rule is expanded to apply to any slaughter. The Oral תּוֹרָה Torah preserves the methods by which a כָּשֵׁר kosher animal must be slaughtered in order to be כָּשֵׁר kosher for consumption. If the animal is killed in any other manner, let alone dies of natural or predatory causes, it is not כָּשֵׁר kosher. The prescribed methods ensure that the animal is treated well and suffers briefly (if at all) before falling unconscious.
שחיטה Shechita requires that the animal be healthy and viable; it may not be injured, as most big cattle farms do when they shock the animal. The animal must be killed be quickly cutting both the side of the neck and piercing the esophagus. This causes a sudden drop in blood pressure and is loses consciousness within a few brief seconds. Next the animal must be drained of blood.
כִּי-יִרְחַק מִמְּךָ הַמָּקוֹם, אֲשֶׁר יִבְחַר יְהוָה אֱלֹהֶיךָ לָשׂוּם שְׁמוֹ שָׁם, וְזָבַחְתָּ מִבְּקָרְךָ וּמִצֹּאנְךָ אֲשֶׁר נָתַן יְהוָה לְךָ, כַּאֲשֶׁר צִוִּיתִךָ--וְאָכַלְתָּ, בִּשְׁעָרֶיךָ, בְּכֹל, אַוַּת נַפְשֶׁךָ.
[That - far off when you place YHWH your God in any his name there, and sacrificed to visit you and the flock which YHWH hath given you, as I have commanded thee - and you will eat within your gates, all the desire of thy soul.]
If the place which the LORD thy God shall choose to put His name there be too far from thee, then thou shalt kill of thy herd and of thy flock, which the LORD hath given thee, as I have commanded thee, and thou shalt eat within thy gates, after all the desire of thy soul. Deuteronomy 12:21