Bare-knuckle is a phrase often used to distinguish between boxing with gloves and the more ancient form of combat sport performed by two individuals fighting without any gloves or other form of padding on their hands.
The practice dates back at least to Ancient Greece, but rules for such bare-fisted fighting began to be formulated in the 18th century, when Jack Broughton began to apply rules to make contests both safer and fairer. These rules dictated that a round ended when a fighter took a knee or was knocked down and failed to rise before the ten count. There were an unlimited number of untimed rounds, so the actual fight ended when a fighter could not get up before the count of ten or was unable to present himself to his opponent for the next round under his own power after thirty seconds of recovery. This was how a majority of these bouts ended. Fights lasting 60- 100 rounds or more were not uncommon.
Tom Cribb was one of the most notable bare-knuckle boxers of the early 19th century. Less than 100 years later, the practice had all but disappeared, replaced by much more regulated gloved bouts. However, some underground boxing clubs do still exist. Many small ones popped up in the late 1990s and early 2000s, inspired by the club from the novel and movie Fight Club.
From Main Wikipedia: 
See also, Origins of Boxing