Question

what happens to a ball from the time it is dropped to the time it reaches its first rebound height.

Answer 1

When the ball hits the floor, its center of mass needs to be decelerated. It is done by deforming the ball (and possibly the floor if it is soft enough compared to the ball). In vacuum, if the ball and floor were perfectly elastic, they would then recover their previous shape following exactly the reverse dynamics as the deformation ones: in doing so, the center of mass of the ball would be accelerated of the exact same amount it has been decelerated, thus it would bounce back to the same height.

However, nothing is perfectly elastic: there is some friction during deformation (solids are somewhat viscoelastic), dissipated as heat, and there's also damage (plastic deformations: if the ball is hard, it will notch or chip bits off the floor e.g.) This energy is not recovered when the ball takes back its original shape.

As Jim notes, another loss is due to friction with air: although this is generally small for a ball heavy enough, this would still prevent bouncing back to the same height. It occurs both during fall and rise, and when hitting the ground: that's when the sound of the ball hitting is produced.