What exactly is Einstein's mass-energy equivalence ( E = mc2 )?

One of Einstein's greatest insights was to realize that matter and energy are really different form of the same thing. Matter can be turned into energy and vice versa.

Einstein's formula tells us the amount of energy any mass would be equivalent to, if it were all  turned into energy. It says that to find the energy, we multiply the mass by the square of the speed of light, this number being 300,000,000 meter per second:

= m x 300,000,000 x 300,000,000 =  90,000,000,000,000,000m Joules

This theory can be explained by the following example:
  The masses of all the stable nuclei are less than the sum of the masses of their constituent particles (protons and neutrons) in the free state. This means that when the protons and neutrons combine to form a nucleus, a loss of mass takes place. The missing mass is released in the form of energy when the nucleus is formed.

If m be the missing mass in the formation of a nucleus, the energy released E will be given by Einstein's mass-energy equivalent relation

                                                                E = mc²

where, c is the speed of light. 

The missing mass (m) is called the mass defect and its energy equivalent (E) is called binding energy of the nucleus. Here E is the actual energy that must be supplied to the nucleus to break into its constituent particles i.e. protons and neutrons.