e = mc^2, where m is rest mass is only part of the total energy equation. The whole equation is this...
E^2 = e^2 + k^2; where E = Mc^2, e = mc^2, and k = Mvc and c is light speed. The k is relativistic kinetic energy, where M = m/sqrt(1 - (v/c)^2) is sometimes called relativistic mass. Rest mass m is the ordinary mass you and I are used to seeing every day.
If you let v = c, so the mass m is going light speed, the total energy equation becomes E^2 = e^2 + E^2; so that e^2 = (mc^2)^2 = 0 = E^2 - E^2. The only way that can happen since c > 0 always is for m = 0.
And that's the crux of it all. Rest mass m > 0 cannot go light speed no matter how small that mass might be. The only thing that can go light speed (v = c) is something with mass m = 0, like photons that are massless.
So going at or above light speed is impossible if there is the slightest bit of rest mass m.
As to what e = mc^2 means, it means mass and energy are equivalent, which is why we often use the term "mass-energy" because it makes no difference if we use m or e in totaling up energy in a system. And it means the energy is proportional to the rest mass with the constant of proportionality as c^2.
And that's all c^2 is... a constant of proportionality, it does not mean that m is going at any velocity, let alone c. In fact, as we see from the E^2 equation m is really the rest mass, meaning its relative velocity v = 0. And e = mc^2 remains the same no matter how fast m is going. What increases the energy level is the kinetic energy k = Mvc as m's velocity goes from v = 0 toward v ~ c.
You might call mc^2 the potential for energy because mass can be converted into all kinds of energy, including heat, light, blast, EMF, kinetic, etc. But e is that energy, not the potential for it.
One more point, e = mc^2 points out that rest mass and energy are equivalent. But it does not indicate they are the same thing. Clearly mass and energy are not the same thing. Mass, for example, is a source of gravity; energy in general is not.