Potential energy is the energy that an object has the potential to use. Potential energy is usually figured from gravity. Gravity is an acceleration, and the object has a mass, so the force gravity has on an object can be calculated. Using this force we can determine the potential energy of the object. It is the distance the object is from the ground multiplied by the force of gravity.
Kinetic Energy, is the energy that an object uses to move. The equation for Kinetic Energy is KE = 1/2mv^2. The energy of a moving object is easily found using this equation, as long as the mass and velocity are known.
A steel ball flying at 10m/s with a mass of 1kg would have 50 Jewels of energy (KE = 1/2 * m * v^2; 1/2 * 1kg * 10^2m/s = 50J). If there object were 10 meters from the ground, it would also have 98 Jewels of Potential Energy (PE = F * D; F = m * a; a = g, m = 1kg; g = 9.8; PE = 1kg * 9.8m/s * 10m = 98J). The total Energy would then be the PE and the KE, so 148 Jewels.
This might not seem important right now, finding the energy, big deal, whats it used for? It can be used through the conservation of energy. Energy will always be conserved unless some outside force acts on the system. Using the flying ball example, this ball would start with both Kinetic and Potential Energies. If the ball fell due to gravity and hit the ground, then the Potential Energy would be zero since the distance that was used to figure the Energy now became zero. So the Potential Energy was used up as Kinetic Energy which was needed for the object to move. So the Kinetic energy when the ball hits the ground would be 148 Jewels. The total energy in the system, thus, would still be 148 Jewels.
This is very useful for when objects collide. In ellastic collisions, not only is momentum conserved, but energy is conserved as well. The equations for this conservation are just all the energies before and after:
Energy before = Energy after
PE + KE before = PE + KE after
This equation in combination with the conservation of momentum can be used to calculate what momentum, energy, force, velocity, accelerations are passed from one object to another in a collision. This is a must in a CGE if any objects should act realistically on each other.