Why does E=mc^2?

Thank you all, for trying to help me “get” it. I understand the very straightforward definitions of “work” and “force”, and Pasta got me to a breakthough by pointing out that kinetic energy also involves velocity squared, which is precisely the idea that I’m trying to wrap my brain around.

So I found this in the Wikipedia article on Kinetic Energy:

By dropping weights from different heights into a block of clay, Willem 's Gravesande determined that their penetration depth was proportional to the square of their impact speed.

Aha! So if I drop two equal weights, and one has triple the speed at impact, it will penetrate nine times as far? Okay, now I have to digest this a bit… Thanks!

Depends. For instance, see the description of Newton’s approximation of the impact depth of a blunt, high-velocity penetrator: as long as it is going fast enough to plough through the target, the penetration distance will not depend on the velocity at all.