The yellow star at the centre of Earth's home system, whose gravity the Enterprise and a captured Bird-of-Prey use for the slingshot manoeuvre that makes time travel possible.
Sol, usually called simply the Sun, is the star orbited by Earth, Mars and the other planets of the Sol system, the region Starfleet designates Sector 001.
Its chief dramatic role is as the anchor of the slingshot effect, in which a starship dives towards the star at high warp and breaks away to travel through time. The Enterprise uses it to return from the 1960s in the Original Series episode Tomorrow Is Yesterday, having first met the effect by accident, and Kirk's crew repeat the feat in a Klingon Bird-of-Prey in Star Trek IV: The Voyage Home, both to reach 1986 and to come home with two humpback whales.
In the same film the alien probe's transmissions cut off the sunlight reaching Earth, and in the Voyager story Future's End a temporal explosion destined to destroy the whole system in the twenty-ninth century drives the plot.