In this exhibit, the energy and momentum of the incoming balls is transferred to the outgoing balls. Energy and momentum are physical quantities which are precisely conserved, meaning they do not change over time. Energy comes in many forms and sometimes will change from one form to another. However, because the balls are very hard, little of the energy of motion (kinetic energy) is converted in the collisions into other forms of energy like heat energy. Momentum does not come in different forms and depends only on the mass and velocity of the bells. The conservation laws restrict the possible outcomes of the collisions and leads to the behavior observed.
Energy is a measure of the ability to do work. Energy is why you put food in your stomach and gas in your car. Momentum is a measure of mass in motion and has a direction. Momentum is the reason you wear a seatbelt in your car.
Isaac Newton was a great scientist who discovered the laws of motion that apply to this exhibit and to many other things like the path of a ball through the air, the internal dynamics of the engine in your car, and even the motion of our planet around the sun.