Drum brakes work on the same principle as disc brakes i.e. shoes press against a spinning surface. In this system, that surface is called a drum.
When you step on your brake pedal the two curved brake shoes, which have a friction material lining, are forced by hydraulic wheel cylinders against the inner surface of a rotating brake drum. This contact produces friction causing the drum and the wheel to slow down or stop.
Many cars have drum brakes on the rear wheels and disc brakes on the front. Drum brakes have more parts than disc brakes and are harder to service, but they are less expensive to manufacture, and they easily incorporate an emergency brake mechanism.