From the cosmic perspective, 'mass' is energy in a state that, instead of traveling at the speed of light, wants to sit on one place (for reasons that were discovered later), and needs a push to get it moving. When you measure mass, you're really measuring how much you need to push a given amount of this inertially-fixed energy to impart a given velocity. Our ordinary units of energy, mass, and velocity came from observing these facts of physics before we figured out what mass and energy "are", and E=mc^2 ties the knot between the different units we came up with.
The really fascinating thing is that Einstein was able to propose E=mc^2 before any of that was known. It was just a funny term that showed up in the equations for relativistic energy and momentum, and somehow Einstein's intuition was that it might mean something more.
Can you recommend an idiot-friendly source to read about this mass-energy relationship in more detail?
It is one of the assumptions of Einstein, namely that there is a fixed max velocity c. To get Newton's 1/2mv^2 in the Taylor expansion requires a factor c^2.
Something else would lead to measurable deviations in slowly moving objects.
When deriving this formula for the energy it becomes clear that _any_ multiple of ymc^2 is conserved. We choose E = ymc^2 and not, say, E = 5ymc^2 because in the Newtonian limit (as speeds approach zero), the ymc^2 formula reduces to the well-known E = 1/2 mv^2, which is the kinetic energy of an object obtained from classical mechanics.
I'd really recommend reading a mathematical treatment of special relativity, because you'll be exactly clear on where this formula comes from.
You can answer the "how" very well which is what the mathematical derivation is, and which is what most people are answering in this thread but you see that none of those answers start with "Because..." but rather just keep on spitting out more math. And what we want is an explanation for why c^2 is there and what it means.
We don't know what it means, we haven't answered that question and we don't know how to answer it. It's similar to how pi keeps coming up in a lot of equations and we struggle to understand why.
I'm just an interested lay person, but my understanding is the past century of physics is a giant argument for trusting the math, and accepting it as explanation.
If someone asks "Why does xyz act this way?" then the best answer for it, once you get to non-intuitive quantum scales is: "because the math says so." Dirac's prediction of the existence of antimatter, the Higgs, and pretty much all quantum mechanical behavior are great examples of this.
Nima Arkani-Hamed, a kickass theoretical physicist, has a great lecture series on the philosophy of physics:
• http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of...
• http://www.cornell.edu/video/nima-arkani-hamed-philosophy-of...
In an aside, he mentions that he used to explain the Higgs field with analogies such like calling it a kind of "molasses" slowing down particles and giving them mass. He's stopped doing that, because the physical analogy is really misleading. The true reason the Higgs as we conceive of it exists is that it addresses mathematical issues in our treatment of bosons that have mass.
The math said there was an issue. 50 years ago the math said the Higgs fixed it. It took 50 years and construction of the LHC, but now we've verified the existence of the Higgs.
To explain how we figured out the constant is c is a bit more complicated. The wiki article Introduction to Special Relativity is a good way to start if you want to understand everything well.
As for the interpretation thereof, you're going to need someone else.
Another similar question would be why does pi come up in everything? There's a lot of physics where pi comes up and we don't know why.
Likewise, generally speaking, when pi comes up in physics equations it is a geometric factor, either having something to do with the bona fide geometry of the system (e.g. the capacitance of a sphere) or with normalizing some relevant probability distributions. Name one example where we struggle to understand where pi comes from in physics formula!
But still, what does that mean? What does the transmutation of energy into mass or visa versa have to do with the universal speed limit?
I am always struck by the inexplicable power of mathematics to describe the physical laws of the universe, in often simple equations like this. It doesn't have to be that way as far as we know.