Commodity money is to be distinguished from representative money which is a certificate or token which can be exchanged for the underlying commodity. It is not necessary for the commodity itself to have any intrinsic value although it is necessary that the commodity be somewhat scarce.
In situations where the commodity is metal, typically gold or silver, a government mint will often coin money by placing a mark on the metal that serves as a guarantee of the weight and purity of the metal. In doing so, the government will often impose a fee which is known as seigniorage. The role of a mint and of coin is different between commodity money and fiat money. In situations were there is commodity money, the coin retains its value if it is melted and physically altered, while in fiat money it does not.
Commodity money often comes into being in situations where other forms of money are not available or not trusted. Various commodities were used in pre-Revolutionary America including maize, iron nails, beaver pelts, and tobacco. In post-war Germany, cigarettes became used as a form of commodity money in some areas. Cigarettes are still used as a form of commodity money in prisons.
Although commodity money is more convenient than barter, it can be inconvenient to use as a medium of exchange or a standard of deferred payment due to the transport and storage concerns. Accordingly, notes began to circulate that a government or other trusted entity (e.g. the Knights Templar in Europe in the 13th century) would guarantee as representing a certain stored value on account. This creates a form of money known as representative money.
Historically gold was by far the most widely recognized commodity out of which to make money: gold was compact, easy to work into more beautiful jewelry, had decorative and functional utility as a finely strung wire or thin foil leaf, and most importantly, could always be traded for other metals to make weapons with. A state could be described as a political enterprise with sufficient land, gold and reputation for protecting both, e.g. the Fort Knox gold repository long maintained by the United States, could reliably issue certificates to substitute for the gold and be trusted to actually have it. Between 1933 and 1970, one U.S. dollar was technically worth exactly 1/35 of an ounce of gold. However, actual trade in gold as a precious metal within the United States was banned - presumably to prevent anyone from actually going up to Fort Knox and asking for their gold. This was a fairly typical transition from commodity to representative to fiat money, with people trading in other goods being forced to trade in gold, then to receive paper money that purported to be as good as gold, and then ultimately see this currency "float" on commodity markets.
The theory of natural capitalism and of global resource banking have more recently been used to suggest a form of money based on ecological yield. While this would be based on water, air, kilowatts of renewable energy or ecosystem products, some of which have a strict commodity definition, such goods cannot be held directly, and so it is more common to suggest that representative money be issued based on enhancing and extending nature's services, giving one the right to receive the yield as benefit.
Critics of this type of proposal often note that, as with other transitions from commodity to representative money, inadequate substitutes will be made on a "just trust me" basis - as per Gresham's Law which states that bad money dries out good. Other proposals, such as time-based money, rely on the availability of human labour as a commodity, especially within a community, which is presumably harder to guarantee access to, but also harder to steal. Still others deny the utility of commodifying labour as such, and suggest making free time the standard, since physical capital used for leisure, sport, art, theatre, and other forms of play is commodifiable and possible to control. Amartya Sen in Development As Freedom discussed the relationship between access to commodities, labour, and "the right to live as we would like".
It is hard to imagine a physical commodity which would again serve as money.