This is a simple fact that arises from Einsteins theory of special relativity. The theory brings out perhaps the most famous equation of all time.
E=MC^2
Now we can see from this very simple equation that mass and energy are the same thing in different forms. In fact some theories such as Unified field theory can describe mass as literally the movement of field lines by energy. (which is like a load of strings set out evenly and when you push some together they form a particle of mass)
Anyway this equation has changed our world in so many ways. It prohibits us travelling at the speed of light, it created nuclear bombs, it created nuclear energy in the form of fission and the possibility of fusion. It explains how our sun provides us with light and energy.
Most importantly of all we now know that if you stretch an elastic band, it gets more massive. Which when you didnt think about it seem absurd but when looking at the equation makes sense. You add energy to the band, the band stores the energy as mass.
Though to be fair the mass increase is incredibly small.