Money used to be backed by gold and may now be backed by other securities, but I'd like to suggest that the real reason money (or gold itself, or other securities) has value is because it's backed by sex. Maybe it's just the amateur population geneticist in me, but biologically just about everything comes down to sex, even abstract social constructs like money.
Money(/gold/whatever) has value because it can be converted to sex. Money serves a complementary biological purpose for both genders: men want to have sex as much as possible, and women want to have their children protected and provided for -- and money can help them accomplish both. Not directly, of course, unless you're inordinately attracted to portraits of Alexander Hamilton and Adam Weishaupt or can build a shelter out of tiny pieces of paper, but indirectly because people are willing to perform sex-related services (such as getting married) in exchange for wealth and its accoutrements.
Prostitution is often considered "the oldest profession", and it's also the most direct tie between money and sex. Even before there was money, wealthy nobles would send their daughters off to marry the sons of other nobles, trading sex for protection and prosperity. Are many modern marriages much different than long-term prosititution in exchange for food and shelter?
Money is to humans what plumage is to peacocks, and ultimately it's most important purpose is to attract a high-quality mate. As long as it's successful in this it needs no other intrinsic value.
Part 2 goes into more detail and refutes some criticisms.