A compound fracture was an injury that occurred when there was a break in the skin around a broken bone.
In 2269, after being miniaturized by spiroid epsilon waves, Hikaru Sulu suffered a compound fracture of the leg after falling from a console top on the USS Enterprise. (TAS: "The Terratin Incident")
In 2372, The Doctor mentioned that he had healed eleven compound fractures since he was first activated the year before. (VOY: "Lifesigns")
In 2373, after having sex with Grilka, Quark had a compound fracture of the right radius, along with several other injuries. (DS9: "Looking for par'Mach in All the Wrong Places")
In 2374, Kellin was left with a tibular compound fracture after a bulkhead on her vessel had fallen on her. (VOY: "Unforgettable")