A resilient nylon tarp supported by springs in a metal frame. It is supposed to be used as a springboard and landing area in tumbling or acrobatics. It is more often used by children as a place to bounce and play or, sometimes, to fall off of, sustaining head injuries and broken limbs.
Adults could use a trampoline for -- ahem -- other activities, but I wouldn't advise it. You're very likely to get injured, and the guys in the ambulance will laugh at you.