An afterburner is an extension of a jet engine, used in military aircraft. It injects fuel into the heated exhaust pipe of the engine. It will react with uncombined oxygen in the exhaust, which increases the exhaust temperature and, thus, its velocity, giving the plane additional thrust.
The only civilian aircraft using afterburners is the Concorde.
Afterburner is also an album by ZZ Top. See Afterburner (album).