The credit is the main unit of currency in use by the United Federation of Planets in the fictional Star Trek universe.

The actual day-to-day workings of the Federation economy has never been laid out in detail, but credits have been mentioned in several episodes of various Star Trek shows as a form of currency. Based on some of the dialogue in these episodes (and some of the movies) which suggests that the Federation does not use money - unlikely on its face, as it would not be possible to operate an efficient economic system, particularly one encompassing thousands of worlds, without some form of exchange - it seems likely that the Federation credit is not a form of physical currency (like a coin or paper bill), but rather one that exists in the cyberspace of the era. Meaning, Federation credits would be all-electronic - not existing as physical objects, but still as some form of monetary unit that can be paid as necessary.

For example, in Encounter at Farpoint - the pilot episode of Star Trek: The Next Generation - Dr. Beverly Crusher is seen buying an exotic piece of fabric from a shopkeeper on an alien world. She tells the shopkeeper to put it on her "account", suggesting this very form of exchange. In an episode of Star Trek: Deep Space Nine, Benjamin Sisko speaks of his time at Starfleet Academy when he quickly used up his allotment of transporter credits, due to his habit of beaming back to his home every night for dinner. Also, another ST:TNG episode featured William Riker cashing in his substantial store of Federation credit vouchers in order to get Quark to give him information.

In Star Trek: Deep Space Nine, it is apparent that Federation credits are not widely accepted outside of the Federation itself. In such cases, latinum - a valuable metal invented by the Ferengi (and impossible to duplicate via replicator) - has become the generally accepted medium of exchange.

Also, in the bar on DS9 owned by Quark, there is the equivalent of an ATM machine which can exchange and dispense the various forms of currency used by the various races which frequent the station (Federation credit vouchers, Cardassian leks, Bajoran litas, Klingon darseks, and so on).