What is magic?

Any sufficiently advanced technology is indistinguishable from magic.

Arthur C. Clarke

I believe the above quote is much more insightful than most people realize. Many people, myself included at first, pass it off as merely witty or "cute". But to me, it raises profound issues about just what magic is, and if there even can be such a thing as magic.

Many people tend to define magic as some variation on "What can't be explained". But explained by whom? If I somehow carried a flashlight 500 years back in time, would it be magic? It would certainly seem magical to the people of the time, but is that enough to make magic? The word loses its, well, magic, if you make it depend on timeframe...

Clarke's quote suggests that advanced technology is indistinguishable from magic. But, that means it still isn't magic, just really hard to tell apart from it. But if it's indistinguishable from it, you can't tell the difference. So what is the difference? What is the essential difference between magic and something we just don't understand yet?

Even more generally, and relating to the previous post, can there even be such thing as the "supernatural" at all? If it exists in our world at all, doesn't that make it natural by definition? We might not be able to immediately explain it, but that doesn't make it any more supernatural than unexpected results from some scientific experiment.