A bouncy ball touches the ground for a teeny amount of time. First it squishes. Then it unsquishes. Energy of motion goes into squishing the ball in the first part and into throwing the ball back up in the second part. For a less bouncy ball, the energy that goes into squishing spreads around and mostly doesn't get together to throw the ball back up in the air. The energy makes the ball a little bit warmer instead.

One reason for this difference could be that one ball is made of a more bouncy material, like rubber, and the other from a more gooey material like gum (try bouncing a round piece of chewed gum). But bounciness also has to do with how the ball is put together. A soft basketball doesn't bounce as well as a pumped up one even though both are made from the same rubber and air. When a soft basketball hits the ground the energy gets spread around and never gets together enough to throw the ball back up in the air.

Bounciness also has to do with the ground. Hard, heavy balls bounce less well on soft ground because their energy gets spread out in the ground and never gets together very well again to throw the ball back up.