E=MC^2

I was listening to some physicists explaining Einstein's equation E=MC^2 ==> Energy equals mass times the square of a maximum velocity squared ==> on this PBS site

Apparently, Einstein initially expressed the equation as M=E/(C^2), and several physicists state that this form of the equation gets more to the heart of what Einstein was communicating - that Mass is a function of the energy of an object. That as you add more energy to an object, you increase its mass, and similarly, when you take away energy you decrease its mass.

I thought these clips, in particular, were good:

Listen:
Sheldon Glashow
The mass of 2 Hydrogen atoms and an Oxygen atom separately is a little bit more than those atoms combined into water H2O, because the H2O molecule is a lower energy state than the separate elements (you have to apply energy to separate Hydrogen and Oxygen.)

Frank Wilczek
Most of the mass of matter as we know it comes from energy. I can't quite get my mind around his comments, but I think he's saying matter by itself doesn't have much mass - but that it's the energy content of that matter that gives it its "heft".

Alan Guth
"What does the speed of light(C^2) have to do with Mass and Energy? Why is this maximum velocity in the equation?"