A commodity money, such as circulating gold coins, has two substantial advantages and two substantial disadvantages in comparison to other forms of money. The first advantage is that it is less dependent on information and trust. Gold was, until modern times, by a substantial margin the densest known metal, and it has several other distinctive characteristics, making it reasonably straightforward to distinguish gold from gold plated lead or even from gold that has been seriously debased by alloys. The value of a commodity gold coin depends on fineness and weight, and weight is easy to measure. So it was practical, indeed common, for multiple issues from multiple sources to circulate together, exchanging at rates determined by relative gold content. Knowing that a coin was from a reliable mint was convenient, but not essential.
The second advantage is that a commodity currency is less subject to manipulation than a fiat currency, whether token coins, such as most currently circulating coinage, or paper money. The issuer of a fiat money can manipulate its value either as a source of income—financing government spending via the printing press rather than taxation—or for other purposes. Inflating a currency benefits debtors, including indebted governments, at the expense of creditors; one reason for Greece's current problems is that, without a currency of its own, it does not have the option of that form of de facto default. And manipulation of the money supply can be used for other political purposes, such as temporarily lowering the unemployment rate via an unanticipated expansion. Thus the value of a fiat currency is potentially less predictable than the value of a commodity currency, and predictable value is an important feature of the currency in which parties contract for future payments.
The flip side of this advantage, however, is that the value of a commodity currency is determined by external factors which may themselves be difficult to predict, especially over the long term. New gold discoveries, improvements in the technology for extracting gold from ore, changes in non-monetary demand for gold, all can result in changes in future price levels that are not easily anticipated. Thus the value of a commodity money is less predictable than would be the value of a fiat money controlled by competent and benevolent agents.
The other disadvantage of a commodity money is that someone has to produce the commodity. Labor and capital are expended in locating and mining gold, a real cost. David Ricardo, writing about two hundred years ago, pointed out that a tax on gold mines whose output was used entirely as money in the taxing country and provided all of its money was a burden-free tax—not only did it impose no excess burden (cost to taxpayers above receipts to government), it imposed no burden at all. A smaller amount of gold was mined but the value per ounce was greater, resulting in the same total value of gold money at a lower production cost—and it is the value, not the weight, of money that mostly determines its usefulness. Fiat money represents the limiting case, where "production cost" is in effect all tax.
There is, as I have discussed elsewhere, at least one interesting and attractive intermediate case: A private fractional reserve money. Its value is determined by the value of the commodity on which it is based, so behaves like the value of a pure commodity money; the one difference is that monetary demand plays a lower role, with each ounce of gold supporting the equivalent of multiple ounces of currency. And, for the same reason, it sharply reduces the cost of providing a monetary system compared to the cost with commodity money. But, unlike a pure commodity system, it does depend on trust and information, on being reasonably confident both that your bank note was really issued by the bank it claims to be from and that that bank can be trusted to pay off on its promises.
The reason to raise these issues now is the appearance of bitcoins, a private, decentralized system of anonymous online currency. I have been interested in the subject of anonymous ecash for many years but have no particular expertise in the current incarnation; readers who do are invited to correct any errors in my account.
Bitcoins, as I understand them, are, like gold, mined—not with pick and shovel but with computer power. Each consists of a piece of information which requires a considerable input of computing power to generate. In equilibrium the value of one bitcoin tends to the cost of producing it, just as the value of an ounce of gold tends to its production cost. Thus, like a commodity currency, bitcoins consume real resources in their production. And their value has both the advantage and disadvantage of a commodity money—not subject to deliberate manipulation, but vulnerable to changes from external causes such as reductions in the cost of computing power or mathematical improvements that make it easier to deduce the information used to create one. Like a gold coin, a bit coin can be tested for validity by the user—a process that involves both a check of its mathematical characteristics and the use of decentralized mechanisms to prevent the double spending problem.
The details of how the bitcoin system works should be findable elsewhere online. While I have an avocational interest in the relevant mathematics, I am not an expert in it, so thought it more useful to focus on the economics.