Bitcoin was invented by Satoshi Nakamoto, who must be a skilled and innovative programmer. Anyone can generate bitcoins by setting their computer to solve specific mathematical problems. As more bitcoins are generated, the difficulty of the problems increases. Relatively few vendors currently accept bitcoins, but several dealers are willing to trade dollars for them. And the reason their value has increased must be that people are willing to pay more dollars than previously.
Why pay more dollars? One reason is that the total number of bitcoins is limited, so presumably they cannot suffer the kind of inflation that often occurs with paper currency. (Could that rule change? Yes, just as some new major deposit of gold or silver might be discovered.) Another reason, of course, could be that people are just learning about bitcoins, and seeing the trend, expect it to continue. Also, bitcoins give some indication of being truly anonymous, secure money.
Now, if I was a skilled programmer, I could invent my own bitcoin-ish system, and generate my own coins. But unless someone is willing to accept my coins in exchange for something people want, they’ll have no value. Perhaps Satoshi Nakamoto is not only skilled, but also charismatic.
Bitcoins have intrinsic value in the sense that it takes a lot of work (done by the computer) in order to generate one, much as it takes a lot of work to discover, mine and refine precious metals. But, whereas I could use precious metals to make jewelry or tableware, I can’t think of anything that anyone could do with a bitcoin, other than spend it or save it.
So it seems to me that bitcoin shows that fiat money could work quite well, provided that the proper amount of it is issued. If bitcoin’s deflationary trend continues, it might be a good investment but would lose usefulness as actual currency. I think the most likely outcome will be, either, a decision to produce more bitcoins (however that might be made), or the creation of other alternative currencies operating in parallel.