No one has answered your question. There is no answer really to your question. At least, not to the level that you are asking. Why is c^2 in that equation? What does it mean? We don't know. It's a deeper level of understanding that we haven't achieved.
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.
The original question has perfectly satisfying explanations accessible to anyone who knows algebra and is willing to spend a few weeks studying special relativity. cynicalkane above provides a great intuitive summary.
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!
I strongly disagree. We don't know the answer to everything, but we have solved this question - in terms of other, more fundamental things that we haven't fully explained yet. It would be disingenuous to pretend that because we have solved the deeper layer, we can't give an answer at the shallower one.
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.