Disc brakes (click link for photo), sometimes spelled as “disk” brakes, use a flat, disk-shaped metal rotor that spins with the wheel. When the brakes are applied, a caliper squeezes the brake pads against the disc (just as you would stop a spinning disc by squeezing it between your fingers), slowing the wheel.
Drum brakes (click link for photo) use a wide cylinder that is open at the back, similar in appearance to, well, a drum. When the driver steps on the brake pedal, curved shoes located inside the drum are pushed outwards, rubbing against the inside of the drum and slowing the wheel.
Disc brakes are generally considered superior to drum brakes for several reasons. First, they dissipate heat better (brakes work by converting motion energy to heat energy). Under severe usage, such as repeated hard stops or riding the brakes down a long incline, disc brakes take longer to lose effectiveness (a condition known as brake fade). Disc brakes also perform better in wet weather, because centrifugal force tends to fling water off the brake disc and keep it dry, whereas drum brakes will collect some water on the inside surface where the brake shoes contact the drums.
All cars sold in the United States use disc brakes for the front wheels, but many cars still use drum brakes in the rear. Braking causes the car’s weight to shift forward, and as a result about 70% of the work is done by the front brakes. (That’s why your front brakes tend to wear out faster.) By fitting disc brakes to the front wheels and drum brakes to the rear wheels, manufacturers can provide most of the benefits of disc brakes while lowering costs. (Drum brakes are less expensive to make than disc brakes, largely because they can also double as a parking brake, whereas disc brakes require a separate parking brake mechanism.) Even so, a car with four-wheel disc brakes (versus front disc/rear drum) will still provide superior braking performance in wet weather and on long downgrades. (That said, you should always downshift and let the engine control the car’s speed on long downgrades.)
If your car was built in the last thirty years, it most likely has disc brakes on the front wheels, but it may have drums in the rear. If the car has wheels with big openings, you may be able to see some or all of the brake assembly. Seen through the wheels, disk brakes look like this, with a flat rotor set back from the inside surface of the wheel and a wider piece (the caliper) at the front or rear of the disc. Drum brakes look like this, with a cylindrical drum that is usually flush against the inside surface of the wheel.