Of the “beasts of the earth” (which basically refers to land mammals with the exception of swarming rodents), you may eat any animal that has cloven hooves and chews its cud. Lev. 11:3; Deut. 14:6. Any land mammal that does not have both of these qualities is forbidden. The Torah specifies that the camel, the rock badger, the hare and the pig are not kosher because each lacks one of these two qualifications. Cattle, sheep, goats, deer and bison are kosher.
Of the things that are in the waters, you may eat anything that has fins and scales. Lev. 11:9; Deut. 14:9. Thus, shellfish such as lobsters, oysters, shrimp, clams and crabs are all forbidden. Fish like tuna, carp, salmon and herring are all permitted.
For birds, the criteria is less clear. The Torah provides a list of forbidden birds (Lev. 11:13-19; Deut. 14:11-18), but does not specify why these particular birds are forbidden. All of the birds on the list are birds of prey or scavengers, thus the rabbis inferred that this was the basis for the distinction. Other birds are permitted, such as chicken, geese, ducks and turkeys. However, some people avoid turkey, because it is was unknown at the time of the giving of the Torah, leaving room for doubt.
Of the “winged swarming things” (winged insects), a few are specifically permitted (Lev. 11:22), but the Sages are no longer certain which ones they are, so all have been forbidden. There are communities that have a tradition about what species are permitted, and in those communities some insects are eaten.
Rodents, reptiles, amphibians, and insects (except as mentioned above) are all forbidden. Lev. 11:29-30, 42-43.
Some authorities require a post-mortem examination of the lungs of cattle, to determine whether the lungs are free from adhesions. If the lungs are free from such adhesions, the animal is deemed “glatt” (that is, “smooth”). In certain circumstances, an animal can be kosher without being glatt; however, the stringency of keeping “glatt kosher” has become increasingly common in recent years, and you would be hard-pressed to find any kosher meat that is not labeled as “glatt kosher.”
As mentioned above, any product derived from these forbidden animals, such as their milk, eggs, fat, or organs, also cannot be eaten. Rennet, an enzyme used to harden cheese, is often obtained from non-kosher animals, thus kosher hard cheese can be difficult to find.