Bouncy balls bounce high because the material of the ball is extremely elastic and can convert the kinetic energy from the fall into potential energy and back again with very little loss in momentum. Bouncy balls are used in many physics classrooms because they aptly demonstrate conservation of momentum through a highly elastic collision.
Bouncy balls, also called superballs or rubber balls, are toys that were developed in the mid-20th century. They are made out of a synthetic rubber known as polybutadiene. Like many things made out of rubber, bouncy balls have very high elasticity, meaning they rapidly return to their resting state after being stretched or squashed.
If a bouncy ball is dropped onto a hard surface, it flattens somewhat as it contacts this surface, and the kinetic energy of its motion is converted into potential energy. This is very similar to the potential energy stored in a spring that gets compressed; once it is released, it pushes out with energy equal to what was required to push it in but in the opposite direction. The potential energy of the bouncy ball converts back into kinetic energy, which is applied in an equal and opposite direction to the force that originally caused the collision. If a bouncy ball is dropped instead of thrown, it bounces back up to almost the same height from which it was dropped. If not for the energy lost due to friction in the air and on the surface contacted by the ball, it would keep bouncing.