On this Moment of Science we answer the question: Why does a well-inflated basketball bounce higher than a ball with less air?
Air molecules are naturally elastic--they don't stick together like water molecules, but rather bounce off each other in the open. When tightly packed together inside a basketball, air molecules form a sort of highly elastic unit of air. Think of the air inside a basketball as a tightly coiled spring. The tighter the spring, the more energy it has to bounce back up. The same applies to air: the more air inside the ball, the harder it pushes back against the ground, springing the ball into the air.
The ball's skin, whether rubber or leather, is less springy than the air it contains. When the skin of a basketball hits the ground it deforms, or flattens. This flattening converts the ball's energy into heat, just like how a rubber band gets hot if you quickly stretch it several times. The amount of the ball's energy that converts to heat is lost energy--it contributes nothing to making the ball bounce.
Logically, the more the ball's skin gets pushed in, the more energy is lost to heat. The more air inside the ball, the less the ball compresses upon impact. And the less the ball flattens, the more energy there is to make the ball rebound. Of course, an inflated ball won't keep bouncing with the same force for very long. Each time the ball impacts the ground it loses a bit more energy, until so much of it's energy is spent that it stops bouncing completely.