Bitcoin is a form of cyber-money that has been with us since 2009. In order to understand it, and why it may or may not be interesting, it helps to review other more or less conventional monetary arrangements. The three I've chosen, as each shares something with bitcoin, are commodity money, fiat money, and private money.
The earliest forms of money were commodity monies, primarily gold and silver. It's not hard to see why gold makes a good commodity money. It is scarce, it is difficult to replicate (i.e. counterfeit), and it is relatively easy to carry around, at least in the quantities one would need to make day-to-day transactions. The scarcity comes from the fact that it is costly to dig the gold out of the ground, and its physical characteristics make counterfeiting costly as well. These properties of gold of course did not prevent people from trying to scam the system. Alchemists tried in vain to create gold out of nothing (or, one step up, urine), and counterfeiting and debasement made quality-monitoring necessary.
Commodity money systems were not without their costs. If gold is used as money, then its value in exchange causes its price in terms of goods and services to be higher than it would otherwise be. There is a "gold bubble" in the sense that gold trades at a price higher than it would if gold were used only as an input in production or for consumption purposes. This higher price of gold makes it more profitable to dig the stuff out of the ground, so there is a resource cost to society of supporting the monetary system. Another problem is that, under a commodity money system, we are at the mercy of changes in technology or in the demand for the commodity for other purposes than as money. For example, if gold is used as money, then a better technology for extracting gold from the ground, or a reduction in the demand for gold jewelry, will reduce the price of gold relative to other goods and services. This is inflation of course, which we know is socially costly.
Modern-day fiat money evolved by way of commodity-backed paper money (e.g. the gold standard). In the US, Federal Reserve notes are not explicit promises to pay anything in the future; the Fed will not redeem the currency it issues in the form of some other commodity or asset. Things are a little tricky though, as the Fed actually lists currency as one of the items on the liability side of its balance sheet, and there are indeed assets on the other side of the balance sheet that represent backing for the Federal Reserve notes. Indeed, the Fed does not create the notes "out of thin air" but issues them in exchange for other assets, which are typically obligations of the US Treasury (though some other stuff currently appears on the asset side of the Fed's balance sheet). Thus, there is a sense in which Federal Reserve notes are ultimately backed by the power of the US government to tax us.
A fiat money standard potentially eliminates some of the costs of a commodity money system. First, paper is cheap to produce and, second, we can solve the problem of price level stability if we can trust the issuer of fiat money to manage the stock of the stuff appropriately. However, we are now faced with some new problems. Counterfeiting now becomes potentially much more severe, which is clearly why it took so long for fiat money systems to evolve. We had to wait for a good anti-counterfeiting technology to arrive. Once it did, the government needed to work continuously to keep one step ahead of the counterfeiters. A good anti-counterfeiting technology is one which makes it very low cost for the average person to tell the difference between a counterfeit and the real thing, and makes it very high cost for a counterfeiter to replicate the real thing (and obviously these two things are related).
Another problem with a fiat money system is that we now have to support an elaborate structure for managing the money supply and monitoring the money-supply managers. The cost of operating the Federal Reserve System and checking up on what it is doing is clearly significant. Sometimes fiat money systems do not work so well, and we get phenomena like this.
There are plenty of examples of the use of circulating private money, typically issued by banks. During the US "free banking era," 1837-1863, state-chartered banks issued small-denomination pieces of paper that were the dominant media of exchange. This era was somewhat chaotic, with many attendant problems, though the success of the system is subject to some debate. Well-functioning private money systems existed in Scotland in the early 19th century and in Canada before 1935. Private money issue in these systems was by no means a free-for-all, as there were well-established rules under which note-issuing banks operated. In the Canadian system for example, it was difficult to obtain a bank charter with note-issuing privileges, the notes were required to be redeemable in gold, and notes were required to be senior claims on the bank's assets. There are modern examples of private monies in North America, which I think we could categorize as curiosities. These include Canadian Tire money and Ithaca Hours.
Now, to get to the point, what is Bitcoin? The orgins of this cyber-money are somewhat obscure, as the author of the underlying code apparently chooses to remain anonymous. Bitcoin is exchanged on an anonymous person-to-person network, which anyone can join by downloading the relevant software from here. The stuff is created essentially by solving a puzzle. I can solve it, you can, or Justin Beiber can solve it, given enough computing power and time. There is nothing creative about solving the puzzle, but it is costly as it burns power (see this) and occupies computing capacity. Further, in creating new bitcoins I have to do some checking of previous transactions on the network, which is in part how good behavior is enforced. A bitcoin is then a string of bits, and it can be traded.
The Bitcoin web site claims that some people are willing to accept bitcoins in exchange for goods and services, and some are willing to exchange bitcoins for US dollars (and presumably other currencies). The algorithm is designed so that solving puzzles becomes progressively more difficult, which targets the growth path of bitcoins so that the quantity converges to 21 million in about 2140.
Bitcoins share some of the features of a commodity money, in that there is a natural scarcity - the stuff is hard to produce. This comparison helps us think about some of the potential problems as well. What prevents modern-day alchemists from coming up with a way to replicate a bitcoin? Success certainly seems much more likely than for the old-time alchemists, since the bitcoin algorithm was created by a human being. All it takes is a smarter human being to beat it.
A bitcoin is also somewhat like fiat money, in that it is not redeemable. However, in contrast to central bank money, there are no assets backing the stuff. Further, while I can identify Fed officials, and I know how they are appointed, I have no idea who invented bitcoin. How do I know the inventor does not have a second set of software that will allow him to claim all the seignorage when he or she thinks the time is right? While libertarians appear to be attracted by the idea, I don't think the general public will take well to a medium of exchange for which we can't hold anyone responsible. Certainly these people have a problem with it.
One sense in which bitcoins differ dramatically from fiat money is in terms of the anonymity of the transactions. One of the virtues of currency (and also one its downfalls, since this makes it easy to steal) is that it is very low-tech and easy to transfer, and lacks memory. While there is a sense in which the bitcoin network is anonymous, in another sense it is most definitely not. The system tracks the machines on which the bitcoins reside, and appears to record the entire history of such residence.
Like historical private money systems, bitcoin involves a system of private issuers, but the private money systems I discussed above operated within a well-defined legal framework. Any system of monetary exchange requires enforceable rules concerning contracts, and bitcoin has none of this. Further, Timothy Lee, who appears to know what he is talking about, sees a potential collusion problem in the bitcoin system. Whether this is any worse a problem than what existed, for example, in the Canadian banking system pre-1935, I'm not sure.
In spite of the fact that I think bitcoin is a curiosity, on the order of Canadian Tire money or Ithaca Hours, it would be wrong to criticize it for being a "pyramid scheme," or a "bubble." Indeed, modern fiat money is both of those things. One could imagine getting a fiat money system off the ground and observing time series of prices for the stuff that look much like what you can find here. As fiat money becomes more widely acceptable, its price in terms of goods and services rises, and people who "got in early" can make a profit. Fiat money is a bubble in the purest sense, in that its fundamental value is zero, but nevertheless people are willing to give up goods, services, and other assets in exchange for it. Bubbles can be good things, as any asset which is used widely in exchange will trade at a price higher than its "fundamental," and the asset's liquidity premium - the difference between the actual price and the fundamental - is a measure of the asset's social contribution as a medium of exchange.