The short answer
A tagine is both a dish and the pot it is cooked in. The pot is a shallow clay base with a tall cone-shaped lid. The dish is a slow-cooked stew of meat, poultry or vegetables with spices, cooked gently until soft. Classic Marrakech versions are chicken with preserved lemon and olives, lamb with prunes and kefta with egg.
In more detail
The cone is the clever part. Steam rises, cools against the lid and runs back down, so the food cooks slowly in its own juices with little water. In a riad kitchen it often sits over a charcoal brazier. It is served in the pot it was cooked in, with bread to scoop it up.
In Marrakech you will meet three tagines again and again. Chicken with preserved lemon and olives is sharp and salty. Lamb with prunes and almonds is sweet and rich. Kefta, spiced meatballs in tomato sauce, has eggs cracked over the top near the end. Vegetable tagines are on nearly every menu too.
Do not confuse it with tanjia, the city's own dish. A tanjia is a tall clay urn, sealed and buried in the ashes of a hammam furnace for hours. Couscous is different again: fine semolina steamed over a broth, traditionally eaten on Friday.
Learning to layer a tagine so it does not dry out is the heart of most cooking classes in the city, and you eat the result at the end.