E = mc^2 is popularly known as Einstein's Theory of Relativity. Although he did not come up with the formula, he was the first scientist to put it to practical use.
E = mc^2 is mass-energy equivalence. E is for energy, m is for mass, and c is the speed of light in a vacuum. The speed of light (c) is a constant 299,792,458 miles per second. Energy and mass vary, depending on the object.
Mass-energy equivalence means that an object has the same amount of energy regardless of motion. Keep in mind that an object that is not in motion has potential energy, while an object in motion has kinetic energy. As the speed of an object increases, the mass decreases and the energy increases at an equivalent ratio.
The basic goal of mass-energy equivalence is mass conservation and energy conservation. Nature is designed to waste nothing. Energy can neither be created nor destroyed. It only changes form. Following this line of logic, you can determine that mass also can neither be created nor destroyed.
A prime example of E = mc^2 is a nuclear reaction. When two hydrogen atoms are united through fusion, resulting in a helium atom. The resulting helium atom has less mass than the two original hydrogen atoms. Thus, the missing mass gets converted into energy. This concept is also demonstrated through the thermal energy of the sun. Hydrogen is continuously being changed to helium through the process of fusion. The energy is released to warm the earth, and the mass of the sun is compensated by generating more hydrogen.
There is a great book entitled Why Does E=mc^2, and Why Should We Care? It is by Brian Cox and Jeff Forshaw. I read it in 8th grade so it's pretty east to understand and it's also very entertaining. They use many analogies to make it more applicable to everyday experiences, so for a better look at why E=mc^2 i would recommend reading it. (I included a link to Amazon where you can buy it)