Okay let's understand the equation in a simple scenario. I apologize if any of the following has a condescending tone, but I think you are severely confused.
First we will need a definition of Energy. Keeping it simple, Energy is the ability to do work. Now what is Mass? Again not to make things to difficult, I'll be horribly loose and say Mass is what you get when you put something on a weighing scale, a measure of how much gravity is pulling you down.*
Now let's say I work in the Ikata Nuclear Power Plant in Japan. I take a large amount of Uranium and weigh it before I put it in the reactor. Now I put it in the reactor, turn the reactor on and power the whole Ehime Prefecture for a day. I take the stuff out of the reactor and weigh it. I find that the stuff weighs less.
So the Uranium lost some mass and gained some ability to do work (Powering the Ehime Prefecture).
How much ability for work? Well if the mass lost was M, then it would be E = MC^2.
Now you are also asking can this work backwards? Can energy be converted into mass? The answer is yes, but not in a direct sense. You can't have "ability to do work" just hanging around on its own, waiting to be converted into mass. Rather a bunch of particles might reduce their own ability to do work. The lost amount of energy is then the Mass of a new particle, with mass given by E=MC^2. Really I'm skipping a lot here, but a full explanation would involve Special Relativity and some Quantum Mechanics.
*This not what mass is. I'm keeping things simple. Mass is actually not the same as weight.