Rim brakes used to be the most common brakes found on a downhill mountain bike. Now, with the invention of disc brakes, modeled after automotive hydraulic brake systems, they are less common. Rim brakes work as a simple brake system: a brake lever, attached to the handlebars of a mountain bike, is squeezed by the rider when they want to slow down the motion of their bike. this lever is atatched to a cable - the brake cable - that is then attached to two calipers on either side of the front and back wheel rims. Attached to these calipers are pads - brake pads. When the handlebar lever is squeezed, the brake calipers clamp down on the wheel rim, providing enough friction to slow the propulsion of the mountain bike, eventually bringing it to a halt.
Rim brakes will most likely be found on cross country mountain bikes, or mountain bikes that aren't specifically designed for fast, harsh downhill descents. They are efficient, effective brakes, but one must take caution and replace brake pads often, especially if a great deal of downhill braking has occured. Rim brakes are only as effective as the pads that are used - worn down brake pads will not to much to stop a downhill mountain bike in full-speed descent!