I like to think of mass, m, as being a kind of potential energy where energy is the ability to do work or cause a change. And e = mc^2 tells us just how much working energy, e, we can get out of that mass, m.
c^2 is a constant based on the square of light speed c. It does not mean the mass is moving however, in fact we call the mass, m, rest mass because it's the mass when at rest, not moving.
Using today's limited technology and exploiting the e = mc^2 relationship, we are able to convert small portions of mass into energy as heat. And we do that in so-called nuclear power plants. There we convert certain radioactive materials, like uranium or plutonium, into heat that makes steam which drives the generators that make electricity for us to use.
I've kept it simple here. If you want more details, like how the strong nuclear force relates to e = mc^2, ask another question.