A trampoline is a device consisting of a piece of taut, strong fabric

Fabric

A fabric is a textile material, short for "textile fabric".Fabric may also refer to:*Fabric , the spatial and geometric configuration of elements within a rock*Fabric , a nightclub in London, England...

 stretched over a steel

Steel

Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...

 frame using many coiled springs

Spring (device)

A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...

. People bounce on trampolines for recreational and competitive purposes.

The fabric on which users bounce (commonly known as the 'bounce mat' or 'trampoline bed') is not elastic in itself; the elasticity is provided by the springs that connect it to the frame.
A kind of trampolining was done by the Inuit

Inuit

The Inuit are a group of culturally similar indigenous peoples inhabiting the Arctic regions of Canada , Denmark , Russia and the United States . Inuit means “the people” in the Inuktitut language...

, who would toss each other into the air on a walrus skin (see Nalukataq), something like the sheet used by firemen to catch people jumping out of burning buildings.