Ok, to speak on the molecular level I'll specialize to solid rubber balls. When the ball is just sitting around, the long twisty rubber molecules relax into a configuration with low energy. Actually, to be more precise, it's a configuration with low free
energy, which I can define if you want a follow up. That's like a spring sitting in the relaxed position with nothing stretching or compressing it. When the ball hits something, it gets distorted out of shape, meaning that the molecules are forced into some other configuration with higher energy. There's a force pushing back toward the low energy configuration, just like the way a spring pulls or pushes back toward its relaxed length, or like a gravitational force pulls things down toward the lowest point they can reach. That's what makes the ball pop back.
You may be concerned that I didn't describe the lowest energy configuration in detail. Actually, for rubber it's a pretty random-looking tangle, with the details depending on accidents as the rubber is prepared. The point is that whatever that configuration is, that's how the ball chooses to be before it gets distorted, and that's what the restoring force points toward.
(published on 06/27/07)