The nearest star system to the Sun, associated with Zefram Cochrane, who was said to be from there.
Alpha Centauri is the closest star system to Earth, a short hop in galactic terms and an obvious early target for human exploration. In Star Trek it is often used as a symbol of how near the stars are.
Its best known connection is with Zefram Cochrane, the inventor of warp drive. In the original series, he is described as Zefram Cochrane of Alpha Centauri, and in the episode Metamorphosis Kirk, Spock, McCoy and Commissioner Nancy Hedford meet him on a distant planetoid, where he has lived for a very long time with an energy being he calls the Companion.
Alpha Centauri also appears as a waypoint in star charts and in dialogue across the series, as a point of reference for how far humanity has come. Its place in the story of early spaceflight and the first steps toward interstellar travel make it a natural symbol of humanity's reach for the stars.