inertia , it bounces even if u let go of it because of inertia , it is also because u are putting pressure on the ball which puts an equal amount of pressure on ur hand and the ball this is called Newton's third law if u do not know.
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The tennis ball is distorted from its round shape when it hits the ground, which means the volume inside is reduced or the air inside is being compressed. The air then pushes back to restore the tennis ball's original shape and therefore bounces off the ground.
On the way down it is gravity, on the way up it is the weight and material composition of the ball that compresses and expands due to kinetic energy build up.