Plain English Meaning
A small radio device in the aircraft that answers radar signals from the ground. When ATC's radar pings it, the transponder sends back a code that tells controllers which aircraft this is and how high it is flying.
Full Definition
An airborne radio transmitter-receiver that automatically replies to interrogation signals from ground-based secondary surveillance radar. When triggered, the transponder sends back a coded reply containing the aircraft's assigned four-digit identification code and, when Mode C or Mode S is enabled, the aircraft's pressure altitude. This reply allows air traffic control to identify, track, and separate the aircraft on radar.