A Super Toy

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The bigger rubber ball hits the ground before the other one. Then it bounces off and jumps back up in the air. Momentum and velocity of the big ball are reversed. In an ideal elastic collision not one bit of the kinetic energy is transformed into warmth during the deformation of the ball.
The smaller ball, however, is still falling downwards in that moment. This means that hits the other bigger ball which is already moving upwards. The smaller ball bounces off of the bigger ball. During that moment the bigger ball transfers a part of its momentum onto the smaller ball. The smaller ball has a much smaller mass and this means that the additional momentum results in an increase of the small ball's velocity. Because it now moves at a higher, it's kinetic energy is also higher than before. On the other hand, the big ball has less kinetic energy than before. The big ball has passed its energy onto the small ball. Altogether the sum of energy within the system is still the same.
The kinetic energy of the small ball is transformed into potential energy after the collision. The height of the small ball increases and at the same time its velocity decreases. This process continues until the ball's velocity has reached zero. It is the exact moment when the ball has reached its highest point. This point is called turning point. Afterwards the ball falls downwards.
The reason why the small ball reaches this surprising height is the fact that energy was passed from the big ball onto the small ball during the collision.
Here is another example with some figures: If the bigger (lower) ball's mass M is thrice as high as the small ball's mass m, the big ball will stop moving for a moment after the collision, whereas the small (upper) ball bounces off at a velocity twice as much as before and it flies up high in the air. Twice as much velocity means four times more kinetic energy for the small ball. Because of this, the small ball reaches a height which is four times higher than its original height.

On the next page you'll find a nice visualized explanation of this process.