A currency whose value is set by the currency markets; money whose exchange rate relative to other currencies is determined mainly or entirely by unrestricted trading in the currency. Most currencies are
dirty float|dirty floats, which means that the government issuing them attempts to manage their traded value in some way; or else
hard peg|hard pegs, in which the value is tied to something specific.
When a currency is floating, then its value may rise because the county is running a
trade surplus, or it is running a capital account surplus. Floating currencies are not fiat money, although they are often confused for each other.