what actually makes a ball bounce up and down and why?

Let's see. You let go of the ball and gravity yanks it down. It hits the floor with enough force to compress some of the air (or whatever substance) is inside the ball. The air/substance decompresses and expands, launching it back into the air. Gravity doesn't allow it to go as high as the original height from which it was dropped, and it falls again. The process repeats and repeats until gravity finally triumphs and the balls stops bouncing.

It is the materal that determines how well an object bounces. During the collison with a wall or floor, the forces acting on the ball is the normal force from the wall/floor and an a force called impluse from the rapid change in momentum. Since the wall/floor is stationary and considerable massive, the object that hits will experence a great change in velocity.

For example, a ball falling 10 mph (downwards), then bounces back upwards around 9 mph. Since the direction matters, I say down is negative and up is positive so the change in velocity is 9 - (-10) = 9+10=19.

Well, thus such a change creates a force called impluse, which acts on the wall mostly, but from Newtons Third Law this forces eventually acts on the ball.

the ball bounces back and forth

It is because of energy and friction ( restitution )

1) . . . the ball is initially have energy

2) . . it is released so it fall

3) . . . on the ground the energy of the ball is converted to compression of the ball and increasing the air pressure inside

4) . . the energy in air pressure will react to the rubber ball to let the ball to expand

5) . . . the ball will move upward because of the push of the expanding ball

6) . . . the ball will rise to a height lesser than the original height because some of the energy is converted to friction, heat and sound energy

7) process 1 to seven will be repeated until the energy of the ball is dissipated and roll and stop

gravity, law of motion, and potential and kinetic energy are the forces, and the elasticity of the ball is the other factor..

uhh, the bouncy-ness of the ball and because it would be weird if it didnt bounce.

:D

gravity dear

Its momentum

gravity is a factor.