On vehicles with rear drum brakes, the wheel cylinder is the hydraulic actuator that makes the brake work - the drum-brake equivalent of a caliper. It is a small part, but a failing one is a real safety issue. Here is what a wheel cylinder does.
What it does
A wheel cylinder is a small cylinder mounted at the top of a drum brake with a piston at each end. When you press the pedal, brake fluid pushes those pistons outward, forcing the brake shoes against the inside of the drum - see how brakes work and drum vs disc. That is what creates the braking at that wheel.
Only on drum brakes
You will only find wheel cylinders on drum brakes, typically on the rear of older or economy vehicles. Disc brakes use a caliper and piston instead. Many cars have discs up front and drums (with wheel cylinders) in the rear.
Signs of a bad wheel cylinder
The common failure is a leak - the internal seals wear and brake fluid seeps out, showing up as dampness behind the drum or on the tire's inner edge; see brake fluid leak signs. A leaking wheel cylinder soaks the shoes, drops the pedal, and must be fixed promptly.
What to do
Replace a leaking wheel cylinder, and inspect the shoes - contaminated shoes need replacing too; see shoes vs pads. Bleed the system afterward. Keep the front discs healthy with quality pads and hardware.