E - Energy
M - Mass
C - Speed of Light
E = MC^2
Example: (This is a bit sketchy, but you get the idea)
A nuclear bomb (say uranium) explodes. You lose say X amount of mass of uranium. The amount of energy that was released is X time the speed of light squared. Only a little bit of mass needs to be lost for a lot of energy to be released.
The problem is: how do they know how much uranium they have after the explosion?