Ligaments were fibrous, stretchy tissues that connected bones in the body.
In 2371, Walter Baxter strained a ligament in his arm while working out in the gymnasium aboard the USS Voyager. (VOY: "Eye of the Needle")
After having sex with Grilka in 2373, Quark was left with torn ligaments along with several other injuries. (DS9: "Looking for par'Mach in All the Wrong Places")
In 2375, Miles O'Brien's ligaments needed time to knit together with the clavicular joint after Doctor Julian Bashir had repaired his torn rotator cuff. (DS9: "Take Me Out to the Holosuite")
Later that year, Seven of Nine accidentally tore a ligament in William Chapman's shoulder while they were dancing. (VOY: "Someone to Watch Over Me")