The best interpretation is as part of the full momentum-energy equation (letting c=1): E^2 = p^2 + m^2. This simply says that the energy E of a system is a combination of energy due to movement (p) and energy due to mass (m). At rest (p=0) this reduces to E=m, or E=mc^2 if you kept track of units.
> Even masses at rest have an energy inherent to them.
This is a real insight.
> Mass can be converted into pure energy. This is the second meaning of the equation, where E = mc² tells us exactly how much energy you get from converting mass
This is a pop-sci explanation, but it falls apart when you dig a bit. Does F=ma tell you that "force can be converted into acceleration?" Of course not; it tells you that force implies acceleration, and vice versa.
Or: if mass can be converted into energy, then you would have more energy and less mass, so E=mc^2 would no longer hold. It can't be both an equivalence and an exchange ratio.
> If you take a photon and and electron and smash them together, you get a photon and an electron out. But if you smash them together with enough energy, you’ll get a photon, and electron, and a new matter-antimatter pair of particles out. In other words, you will have created two new massive particles.
Later we learn that mass is determined by energy and momentum, both of which are conserved, so mass must be conserved too.