Kosher law divides food into five operative categories. Understanding these categories is the prerequisite for understanding everything else.
Fleishig (meat): Meat from kosher-slaughtered mammals and birds. Fleishig foods require separate utensils, cookware, and serving dishes from dairy, and cannot be consumed in the same meal as dairy. After eating meat, observant Jews wait a period (typically six hours in Ashkenazi practice, less in some Sephardic communities) before consuming dairy.
Milchig (dairy): Any food containing milk, milk derivatives, or manufactured on shared dairy equipment. Dairy products must come from kosher animals. Cheese requires kosher rennet. Milk in some communities must be produced under rabbinic supervision (Cholov Yisrael). Milchig foods cannot be consumed with meat.
Pareve: Neutral foods containing neither meat nor dairy. Eggs, fish, fruit, vegetables, and many grains are inherently pareve. The pareve status of a processed product depends not only on its ingredients but also on the equipment used to manufacture it. A product made on dedicated dairy equipment can carry a "D" designation or "DE" (dairy equipment) notation, warning that it may not be suitable for use with meat meals.
Treif (forbidden): Foods that are prohibited outright, regardless of how they are prepared. This category includes pork and all pork derivatives, shellfish, crustaceans, mollusks, non-kosher-slaughtered meat, blood, certain internal fats (chelev), the sciatic nerve (gid hanasheh), and insects. The prohibition on blood is absolute: even a blood spot in an egg renders that egg non-kosher.
Bishul akum: A rabbinic prohibition on food cooked entirely by a non-Jewish person without any Jewish involvement in the cooking process. This applies primarily to foods that are significant enough to be served at a royal table and cannot be eaten raw. Many commercially produced foods are exempt because they are mass-produced and the concern about social intermingling does not apply, but observant consumers at the stricter end of practice seek "bishul Yisrael" certification for certain categories.