No one knows why the dietary laws (Kashrut) came into being in the first place. They were written thousands of years ago and there is debate over who wrote them. As for what the dietary laws are, here we go:
1) Land Animals: Have to have cloven hooves and chew their cud. Both of these things are required (this excludes pigs which, IIRC, only have cloven hooves)
2) Sea Animals: Have to have fins and scales. Both of these are required, this eliminates, among many things, catfish (only fins). Also, shelfish have neither of these, eliminating them.
3) There is a detailed list in the Torah regarding birds. The rules have been decifered from this list and, IIRC, they include: no birds of prey (probably where you go the carnivours thing from), no feathers on the legs, and a certaing kind of beak is prohibited. However, you are safe eating pultry as long as it is properly butchered.
4) There is only one kind of kodher insect, a king of locust. However, they are no longer identifiable and may be extinct so all insects have been deemed un-kosher.
5) I went into depth on meat and milk in the other thread (Xen's one on veal and beef mixing) so I will not repeat myself unless necessary.
6) Blood is not kosher
7) All animals must be slaughtered kosherly. This means at the right point on the neck with an approprately sharp knife and the animal must have been treated well its entire life. Girafe's, technichely, are kosher, but since it is impossible to find the spot to slice the neck, they are never eaten.
8) Meat has to be salted every couple hours or so for a few days after butchering to draw out all the blood.
9) All meat must be completely blemish free and free from any impurities, much higher than USDA or EU standards will ever be.
10) The entire process from raising to killing to shiping to packaging to cooking (if premade and distributed or restaurant) must be monitored by a rabbi.
11) When cooking, the kitchen must be seperated into meat and dairy sections with certain cooking vessels and utensils for meat and others for dairy. Same with serving dishes and utensils. In restaurants and plants, there are actually two kitchens, one for each.
12) All fruits, vegetables, tubers, and grains are kosher. However, a rabbi must oversee the production of anything made from these things to make sure that nothing is done to make it un-kosher (that's the difference between kosher and un-kosher wine).
13) You can not eat anything from a restaurant that serves unkosher food even if what you are eating is kosher since it may be contaminated or you may be giving other Jews the impression that the place is kohser
14) Certain chemicals, preservatives, ingredient substitutes, dyes, etc. are kosher and some aren't. Those that are are observed throughout the process of manufacturing by a rabbi.
Sorry if I missed anything. As you can tell, there are a lot of rules. Also, an interesting thing to note, the only people besides the Coca-Cola corporation to know every ingredient and the entire process to making Coca-Cola is the Chicago Rabinic Congregation, one of the groups of rabbis that oversee kosher food production. Just an interesting side note.