When light passes by a point in space, these arrows get bigger and smaller. This is the electromagnetic wave passing by. Thus we have fact number two, the E, the electric field that accompanies light, is proportional to a, the acceleration of a charged particle, like an electron. We are getting closer now. The real answer is that no one really knows, but physicists have invented elaborate formulas for calculating energy and discovered an amazing fact.
Energy has many different forms and comes in many different disguises.
Some examples include kinetic energy, which is the energy that an object has because it is moving. It says that if an object has mass m and is moving with velocity v, its energy is given by the above formula. Another kind of energy is potential energy. There is chemical energy in batteries, and nuclear energy is responsible for our bright sunny days. You won't be surprised to learn that light too carries energy, and if you work out the numbers you will find that the amount of energy that light carries is proportional to the square of the electric field.