Energy is hard to define. It is one of those things where you “know it when you see it.” Energy is why things change and move.
In fact, energy is a lot like money:
It comes in different forms (dollars, euros, pesos; kinetic energy, potential energy, chemical energy).
You can exchange one form for another (although sometimes you loose a bit in the conversion process).
You can store it (in a bank; in a battery).
Sometimes it leaves your system (you buy something; you give off heat).
Sometimes it enters your system (you get paid; you are pushed).
However, unlike money the total amount of energy in the Universe is fixed — energy cannot be created or destroyed, it only changes from one form to another. This is known as the Law of Conservation of Energy.
Einstein’s famous equation E=mc2 tells us that matter can be converted into energy and energy can be converted into matter. The conservation of energy still holds — this means that matter (electrons, atoms, people, stars) has a rest energy that can be converted into other forms of energy (kinetic energy, potential energy, or light energy).
Let’s follow a bit of energy as it is converted from one form to another. Inside of the Sun, matter is converted into light energy in a nuclear fusion reaction. The light travels from the Sun to the Earth, where it is absorbed by the leaf of an apple tree. The tree converts the light energy into chemical energy and stores that chemical energy in an apple. A man then eats the apple and converts the chemical energy into kinetic energy, the energy of motion. He climbs to the top of a cliff. As he climbs, he stores gravitational potential energy, the energy something has by virtue of being above the ground. Then, he jumps off of the cliff into the water below, converting that gravitational potential energy into kinetic energy as he falls. He hits the water making a big splash. The kinetic energy of his motion is converted into sound, heat and the kinetic energy of the water.