Bitcoin is having its first "15 minutes" with the recent bubble and crash, but Bitcoin is pretty hard to understand, so I've produced this analogy to give people a deeper understanding of what's going on.
It begins with a group of folks who take a different view on several attributes of conventional "fiat" money. It's not backed by any physical commodity, just faith in the government and central bank which issues it. In fact, it's really backed by the fact that other people believe it's valuable, and you can trade reliably with them using it. You can't go to the US treasury with your dollars and get very much directly, though you must pay your US tax bill with them. If a "fiat" currency faces trouble, you are depending on the strength of the backing government to do "stuff" to prevent that collapse. Central banks in turn get a lot of control over the currency, and in particular they can print more of it any time they think the market will stomach such printing -- and sometimes even when it can't -- and they can regulate commerce and invade privacy on large transactions. Their ability to set interest rates and print more money is both a bug (that has sometimes caused horrible inflation) and a feature, as that inflation can be brought under control and deflation can be prevented.
The creators of Bitcoin wanted to build a system without many of these flaws of fiat money, without central control, without anybody who could control the currency or print it as they wish. They wanted an anonymous, privacy protecting currency. In addition, they knew an open digital currency would be very efficient, with transactions costing effectively nothing -- which is a pretty big deal when you see Visa and Mastercard able to sustain taking 2% of transactions, and banks taking a smaller but still real cut.
With those goals in mind, they considered the fact that even the fiat currencies largely have value because everybody agrees they have value, and the value of the government backing is at the very least, debatable. They suggested that one might make a currency whose only value came from that group consensus and its useful technical features. That's still a very debatable topic, but for now there are enough people willing to support it that the experiment is underway. Most are aware there is considerable risk.
Update: I've grown less fond of this analogy and am working up a superior one, closer to the reality but still easy to understand.
Bitcoins -- the digital money that has value only because enough people agree it does -- are themselves just very large special numbers. To explain this I am going to lay out an imperfect analogy using words and describe "wordcoin" as it might exist in the pre-computer era. The goal is to help the less technical understand some of the mechanisms of a digital crypto-based currency, and thus be better able to join the debate about them.