In equities, "Float" refers to the number of shares available for trading without restriction and stands in contrast to the total number of "authorized shares," which could include uncirculated shares, such as those held in reserve in a corporation's treasury, to ward off takeovers or those authorized for executive compensation. 
In currency markets, the term "floating currency" or "fiat currency" is used to describe currencies that are not backed with hard assets, such as gold or silver and therefore are valued relative to other currencies.
"Dirty float" or "managed float" refers to currencies that are managed by their respective central banks such that the value remains in a prescribed range, typically affected through active buying and selling in the interbank markets.
- The Basics Of Outstanding Shares And The Float. Investopedia.