So, what's a Bitcoin?

http://bitcoin.org/en/faq

It's a private currency created in a way that it cannot be regulated, even by its creator. The closest analogues are the bank notes that were American currency until the civil war. Under that system, different banks would produce their own notes with some nominal value in dollars and then when you took that note to a particular establishment anywhere in the country, they would have a large book, updated daily, to tell them the value of that note locally. It was kind of a pain in the butt, so when the Federal government issued its own notes and sold them to help fund the Civil War, intended as a temporary measure, it was so popular it became what we now know as the US Dollar.

But with computer technology, many of the flaws in that old system are now largely irrelevant. You could have many different bitcoin-like currencies and an app that gives a real-time exchange rate between them so you can use them all together seamlessly.

The downside of an unregulated currency, though, is the inability to put in any stabilizing controls. There is no central bank able to expand or restrict the money supply to ensure a reasonable and steady rate of inflation. As a result, it has been going wildly up and down making running commerce with it a little impractical. Prices fluctuate wildly and so does your wealth if you have money in bitcoins, which can be a real problem for merchants who want to accept them. That may get better as time goes on, but without a central bank, it may not.