E = mc^2 is the energy contained within a particle of mass m, IF it is at rest (has zero velocity with respect to your frame). If it is moving, it's energy is given by E = ymc^2, where y (gamma) is 1/sqrt(1 - v^2/c^2). This may sound like the particle has somehow "gained" or "lost" energy just by switching frames, but so has everything else. The differences in energy have been kept the same, which is all that really matters.

When deriving this formula for the energy it becomes clear that _any_ multiple of ymc^2 is conserved. We choose E = ymc^2 and not, say, E = 5ymc^2 because in the Newtonian limit (as speeds approach zero), the ymc^2 formula reduces to the well-known E = 1/2 mv^2, which is the kinetic energy of an object obtained from classical mechanics.

I'd really recommend reading a mathematical treatment of special relativity, because you'll be exactly clear on where this formula comes from.