ENGINE BRAKING is a method of slowing down an automobile without the use of the car's friction braking system. It works best on cars with a manual transmission, though cars with automatic transmissions experience the effects as well. Some automatic transmissions may compensate for it to some degree, however, which may not be what you want. In the case of either type of transmission (Though it is more useful with a stick) one can downshift in order to increase the effectiveness of this technique, though it can be observed at any time by simply letting off the gas.
If you let up on the gas in your car you will start to slow down. This is in part due to friction. Let off the gas pedal all the way, and you slow down more than you can explain by loss due to aerodynamics and rolling friction, however. The explanation is that your car's engine is no longer putting energy into causing compression, but the road is. Your engine now works specifically as a compressor, being driven by the road, and going through a fairly significant ratio conversion in the process. The compression (and regular friction of course) creates heat, which is dissipated by the engine's cooling system. However, a lot of the energy is also expressed back into the road via the expansion of gases.
There are a number of reasons you might want to engage in engine braking. The first is that it puts little or no more load on your engine than it would otherwise bear, but saves considerable wear on your brakes. This leads into the next reason, primarily in the case of racing, but also when going down long hills; Frequent use of brakes not only wears out the pads but also heats them up. This leads to brake fade (most brake pads do not grip well when hot) and to boiling of the brake fluid, which does not work properly once it has been boiled. Brake fade is only a problem during overuse of brakes, such as going down long, steep hills, or during "aggressive" driving. The third reason, also primarily significant in sports driving, is that you want to decelerate into turns and accelerate out of them. Downshifting increases the effectiveness of engine braking, and increases the number of RPMs at a given speed, which tends to assist in acceleration.
There are two ways to make engine braking more efficacious. The simpler version called an "exhaust brake" adds restriction to the exhaust system, which makes it more difficult for the engine to release the compressed exhaust gases, thus slowing the engine. The upgraded version of this, the Jacobs Engine Brake (AKA the "Jake Brake") found on some commercial diesel engines opens the exhaust valves when the cylinder has been compressed (Or, when it is at or near TDC or top dead center) and releases the stored air through the exhaust system, very loudly. This is the loud "B-R-R-R-R-AP" noise that you sometimes hear large trucks make.
Electric cars also engage in a type of engine braking known as regenerative braking, in which the motor is used as a generator and the batteries as a load. Diesel-electric locomotives also utilize electric engine braking, but instead of storing the power, it is "dumped" into a large resistive carbon element, usually beneath the engine. Attempts to create regeneratively braking hybrid-electric locomotives exist but have so far been generally considered to be failures.