Law of Conservation of Energy
In order to understand the physics behind a bouncy ball, you'll have to first understand the scientific law of conservation of energy: energy cannot be created or destroyed. Instead, energy just turns into another form of energy. So, for example, when you eat a carrot, the heat and light energy put into it by the sun turns into the chemical and electrical energy that powers your body, and enables you to pick things up--for example, a bouncy ball.
Potential Energy
When you throw the bouncy ball into the air, you've transferred some of your energy into the ball. That energy isn't yet going anywhere, it's being held "in potentia" as potential energy, according to the University of Virginia Physics Department. This energy can be held in the bouncy ball indefinitely--it's not going to leak out because of the law of conservation of energy. Only when the ball is released does that energy go somewhere.
Kinetic Energy
Kinetic energy is the energy of motion. Once you drop the ball, that potential energy turns into kinetic energy. Gravity pulls the bouncy ball down, using that kinetic energy to drag the ball down to earth.
Deforming
In the split second when the ball hits the ground, the kinetic energy causes the ball to deform. Here is where the material of the ball comes into play, with a rubber ball, it flattens at the bottom and spreads out somewhat. You'll rarely, if ever, will notice this deformation because it happens so fast.
Bouncing
Rubber is a material that can stretch out, but always tries to return to its original shape. Whenever you squeeze a rubber ball, it always goes back to being ball shaped. If you stretch a rubber band, it always returns to its original size. When a rubber ball hits the floor, kinetic energy spreads out over the floor, then transfers back into the rubber as it returns to its original shape. It does this so fast, it actually pushes against the ground and shoots the ball into the air. A ball made from other material may not do this, according to science museum The Exploratorium. Additionally, some of the energy goes into things like sound and friction against the floor, which is why a ball doesn't always come back to the same height.
According to Wham-O, makers of the Super Ball, the ball is made from a highly compressed rubber-like material that retains 90 percent of its energy when bounced and has a high friction coefficient that allows it to pick up speed on secondary bounces.