A bit was a unit of currency that existed in the form of a coin, which was used in California, United States of America on Earth during the late 19th century. It was equal to one-eighth of a dollar ($0.125), or twelve and a half cents (12.5¢).
In 1893, after inadvertently traveling back in time, Lieutenant Commander Data asked a bellboy at the Hotel Brian for temporary lodging. The bellboy replied that it cost "six bits a day or four dollars a week." Later, when Data joined the local poker game, he was told that the ante was four bits. (TNG: "Time's Arrow")