Kosher, the English pronunciation of the hebrew word 'kasher', means: fit to eat. That said, the concept of kosher encompasses many different forms.
Kosher can be used as a verb - to kosher - a process where blood is drawn out of meat using salt - of course the salt used is...kosher salt. Confused yet?
Leviticus and Deuteronomy speak, in multiple places, as to what foods can and can't be eaten. An animal must chew its cud and have a cloven hoof. These animals are 'clean' - but a horse is unclean, a camel is unclean, a dog is unclean, a pig is unclean.
But, you say, what about fish and seafood? Well, Leviticus and Deuteronomy say - the animal must swim and have fins and scales. If not, it's unclean. That means all seafood and shellfish and some scaleless fish (think catfish) are unclean - sorry, but shrimp, lobster, crab, oysters, clams, squid, are not part of the diet of a Jew who keeps kosher.
The Torah also tells of which birds may not be eaten - typically, birds of prey are forbidden. And, the Torah mentions which insects may be eaten (locusts - yum yum) and that all creepy crawly things are not kosher - or, to use the Hebrew word - trayf.
Now all of this gets even more complex, as there is an additional level of 'kosher' placed on animals. Animals must be properly slaughtered - and if they are not properly slaughtered, they are declared as unclean or trayf - even if they meet the other kosher requirements. So, if you kill a deer (a kosher animal) with a rifle, guess what? If you keep kosher, you can't eat it. It wasn't ritually slaughtered. And ritual slaughter is a 'kosher' thing all to itself with lots of rules and procedures.
But wait, there's more.
Somewhere in either Leviticus or Deuteronomy (I don't remember) is a line that says: Thou shalt not boil a kid in its mother's milk. Kid refers to a baby goat. And over the thousands of years, this poor line has been interpreted by 'the rabbis' and now entails a total prohibition of mixing milk and meat. So, if you keep kosher, no cheeseburgers. No chili - cheese - dogs. No pepperoni pizza (the pepperoni isn't kosher anyway because of pork). This milk and meat prohibition isn't as simple as it sounds. If a food item contains any meat - that means anything derived from an animal - it can't be mixed with a food item that contains any dairy - that means anything derived from milk. So, if you eat a steak for supper, you can't have milk in your coffee for dessert. That breaks the rule. Six hours must pass after eating meat before you can eat dairy. 30 minutes must pass after eating dairy before you can eat meat. Go figure.
Another part of kosher is the strict biblical prohibition against eating blood - hence the koshering operation by using salt (as mentioned above). So, no blood sausage, no blood pudding, and no rare steak.
And, this is just the beginning. There are all sorts of levels of kosherness - dependent upon where you insert yourself into Judiaism. Most secular Jews could care less about kosher rules and eat anything they want. Ultra-orthodox and Hasidic Jews spend countless hours and dollars keeping kosher. Most other Jews fall somewhere in between.