A thrust reverser is a device attached to a
jet engine that deflects the engine's
thrust forward, sort of like a
retro rocket. Usually, thrust reversers are deployed after the
aircraft lands as a parallel to the
brakes: this is why the engines rev up while the plane is
coasting down the runway.
Thrust reversers can also be used when the pilot wants to back up. Few pilots would use them to back away from the gate, however, because of the very real risk that they might malfunction and send the plane crashing through the terminal windows a la Airplane! They are never used in flight... if you need to slow down in the air, you use spoilers.
There are two basic types of reverser. Smaller jet engines usually have a clamshell-like cowling that pops out of the side of the engine, and then swings around the back to deflect the exhaust. On larger turbofan engines, the reversers are relatively smaller, and deflect the exhaust out of the side of the nacelle, rather than around the back.
Virtually all large and medium airliners are fitted with thrust reversers, although many business jets and regional jets don't have (or need) them. Fighter jets and other small high-performance aircraft usually use drag chutes instead of reversers.