It has two variants introduced in Half-Life. The first is seen in Black Mesa's Topside Motorpool, which Gordon uses to reach rooftops and climb over large fences. It is seen later near the entrance to the Lambda Complex, then in several locations around Xen. This variant is useful in said situations, but when the player misses landing on the target elevated surface, he falls and receive a moderate amount of damage.
The other variant is seen only once on Xen, in the first island seen in the chapter Interloper. It is contained in a small hole shut by an aperture-like cover. It opens and closes, allowing any being to fall into the hole. When the aperture opens, the being is propelled outside of the hole. If stuck, it will affect the being's health.
Behind the scenes
The Xen Trampoline texture refers to it as "alien mound". Designer Karen Laur refers to it as "bio sphincter" on her official website.
The Xen Trampoline's effects are not just limited to the player. Grenades, Satchels, Tripmines and Snarks also undergo similar effects. The bullets of weapons including the ray from the Tau Cannon are also directed upwards.
Alien Aircrafts flying over aperture Xen Trampolines on a Xen island.