Before disc brakes became standard, drum brakes did all the stopping - and they are still used on the rear of many vehicles today. They work on a different principle than discs. Here is how drum brakes work.
The basic action
A drum brake has a metal drum that spins with the wheel and a pair of curved brake shoes inside it. When you press the pedal, a wheel cylinder pushes the shoes outward against the inner surface of the drum - see what is a wheel cylinder. The friction between shoes and drum slows the wheel.
Shoes instead of pads
Where a disc brake squeezes pads against a rotor, a drum brake presses shoes outward against a drum - see shoes vs pads and drum vs disc. The shoes have friction material bonded to a curved metal frame and are pushed apart from the inside.
Self-adjusters and springs
Drum brakes use a set of return springs to pull the shoes back when you release the pedal, and a self-adjuster mechanism that takes up slack as the shoes wear. This is why drum brakes have more small parts than a disc setup.
Where they are used
Drums are common on the rear of economy cars and trucks because they are cheap and integrate a parking brake well. They fade more under heat than discs; see brake heat. Keep front discs sharp with quality pads and hardware.