The body of Jewish law concerning what food Jews are permitted to eat.
Kashrut is a noun. Kosher is an adjective. Kosher food is food consistent with the laws of kashrut.
The noun, Kashrut, refers specifically to dietary laws. But the adjective, kosher, can refer to any item or activity that meets the requirements of Jewish law, like a kosher suit, or kosher sex.
Chef Chris had to familiarize himself with the laws of kashrut when he got hired to cook at a kosher restaurant.