Let's suppose I tell you this room is 100 square feet. Pierre, from France, tells you this room is 9.2903 square metres because he uses the metric system. We're both measuring the same physical quantity, the area of the room, but we are just using different units to do it.
We used to think of two separate physical quantites ... one we called energy which we measured with joules or ft.lbs or erg or whatever, and the other we called mass which we measured with kilograms or pounds or whatever.
What Einstein showed was that mass and energy were not two separate things but were one quantity, like area, that we'd been measuring with different units. This quantity we'd call energy if we used energy units to measure it, or mass if we used mass units.
So now there is a physical quantity we call mass-energy. We can use joules or kilograms, ft.lbs or pounds to measure it but it's all the one thing. But just as there is a conversion factor to shift from square feet to square metres, we needed a conversion factor from units of mass to units of energy. That factor is c^2. Mass and energy are the same thing in different units and E = mc^2 is the conversion between those units.