A brazier (BRAYS-yer) is a kind of portable grill, usually made out of clay but sometimes out of bronze or iron, which held charcoal or wood fires. You used it to heat your apartment, or to cook on. The modern equivalent would be a little hibachi.
On a brazier, you could cook the same kinds of things that you cook on top of a stove today. You could fry up vegetables or mushrooms, eggs, or sausages in a frying pan. You could make pancakes or flat breads. You could boil a small amount of water to make tea. And you could put a larger pot on and leave it to simmer all day to make stew, like a crockpot today.
Braziers were widely used throughout the ancient world, from China all across Central Asia and West Asia to Egypt and Rome. They were less common in northern Europe, where most people just cooked over open wood fires. Both wood fires and charcoal braziers were much more dangerous to use than today’s stoves. There were many house fires that got started with someone accidentally tipping over a brazier.
Food in History, by Reay Tannahill (1995). Some good information about Chinese use of braziers, with pictures.