Fencing was an ancient Earth sport where two competitors in protective clothing faced off against each other armed with thin, blunted sword-like weapons. Each of three different weapons (foil, saber, or épée) had different rules. For example, saber was the only weapon where one could use their sword in a cutting motion. The aim of the sport was to score points by making "touches" with the weapon on the opponent's body. The winner was the one who first reached a certain number of points.
In 2258 of an alternate reality, Hikaru Sulu told James T. Kirk that his combat training was in fencing, which he later demonstrated while fighting Romulans with a sword on the Narada's drilling rig over Vulcan. (Star Trek)
Lieutenant Sulu was at one point an enthusiastic fencer. He claimed the sport "tones the muscle, sharpens the eye, improves the posture." In 2266, when he was affected by the Psi 2000 virus, he chased crewmen around the corridors with a foil. (TOS: "The Naked Time")
Captain Jean-Luc Picard was a fencer (an épéeist) and his opponents aboard the USS Enterprise-D included Commander Riker, Lieutenant Dean and Guinan. (TNG: "We'll Always Have Paris", "I Borg", "Lessons")