Kashrut is the word given to the whole set of Jewish food laws, which are found in the Torah. These laws have been developed through the ages by the rabbis.
While there are many Kashrut rules, the two most obvious ones are the avoidance of certain kinds of meat and seafood, and the need to keep meat and milk foods separate.
There are many forbidden foods, including pork, rabbit, horse, frogs and shellfish. All of these, and many others, are not kosher.
All kosher meat from permitted animals, like cows and sheep, must be slaughtered in a special way, which makes sure that the animal suffers as little pain as possible. The method used also ensures that the maximum amount of blood is drained from the meat, since blood is not kosher either. Even a bloodspot in an egg makes that egg non-kosher.
Milk and meat foods are kept completely separate in a kosher home. A kosher kitchen will have separate cutlery and crockery, drawers and shelves, pots and pans for milk and meat foods.
In a kosher restaurant, you will only be able to eat either dairy dishes or non-dairy dishes. In a kosher restaurant that serves meat, for example, you will not have ice cream desserts or milk in your coffee.
Of course, how Jews will cook the kosher food they are allowed to eat will largely depend on the local cuisine.