The sound barrier was the point at which an object started moving faster then the speed of sound. It used to be thought that the sound barrier could not be broken, but Chuck Yeager proved this wrong. Sybok cited this as one example of the unknown which man often feared. (Star Trek V: The Final Frontier)
In 2368, prior to the first flight of the soliton wave rider, Geordi La Forge equated seeing Yeager breaking the sound barrier and Zefram Cochrane engaging the first warp drive to the impending event. (TNG: "New Ground")
The sound barrier was mentioned in a famous deleted scene from Star Trek Generations in which James T. Kirk went orbital skydiving. In the scene, a sound which Pavel Chekov identified as Kirk breaking the sound barrier was the first sign Chekov and Scotty detected of Kirk's approach.