I am not sure if this is the same but I found this world record trampoline act once and it was explained this way.
When a person jumps, off the ground, they contract and extend their muscles, resulting in the jump. The energy comes from chemical reactions in the body that convert stored chemical potential energy into kinetic energy of the muscles. However, not all of that chemical energy is successfully converted into kinetic energy. Some is dissipated as heat, and a significant amount is lost into the ground.
The trampoline, and I assume a diving board, acts as a highly elastic object. An elastic object (like a spring or a bouncy ball) is able to store energy in the form of elastic potential energy. This elastic energy is not lost into the surroundings, and can easily be reconverted into kinetic energy.
Unlike with the ground, each time you jump on the trampoline you get most of your kinetic energy back on the rebound. Therefore, if you keep converting chemical potential energy into kinetic energy by pushing off on each successive landing, you can get some impressively high bounces going.