The value of money is derived from a variety of sources. Essentially, the currency has whatever value people are willing to take it for. If someone is willing to sell a hamburger for one dollar, that dollar has that value, so it's "worth" is not intrinsic, but based entirely on what the system demands. Now, this number is determined by several factors, namely the economic system.
If a community's government and therefore economic system is weak, it will not have a great amount of buying power outside of itself, which weakens the value of its currency (if you are sourcing that hamburger from outside of your community and the community's economy is weak, the price will be driven higher because of the relative expense of the ingredients coming from stronger economic systems).
In many cases, a nation's money supply is backed by something—historically in America it was gold (the gold standard). For about a century, though, since the amount of gold held in reserves is relatively low, the Federal Reserve bank has "backed" the supply of money based on a value they determine—so they "set" the value of money. Overall, however, the strength of the economy is the main determining factor in the value of a currency.