A tagine is a dish - i.e. container/cooking vessel, and a dish you eat - just like a casserole, which is the food AND the container it cooks in.
A tagine has been described as a stew, but it is much more sublime than that. Tagines are slow-cooked dishes, cooked in a covered pot so that the steam and flavors don't escape, and the food stays moist. Traditionally made from heavy earthenware, the tagines were cooked over low heat on a charcoal burner. Now they can be cooked over low direct heat on a stovetop, or in the oven.
The method of cooking in a tagine is North African - you will find them in Algeria, Tunisia, and especially Morocco. Everything cooks tagine style - lamb, beef, chicken, fish, vegetables, even pigeon, turkey, or rabbit.