A shared universe is a literary technique in which several different authors share settings and characters which appear in their respective works of fiction, often referring to events taking place in the other writers' stories. It can also be called a "shared setting." It can be a metafictional device. Shared fictional universes tend to appear more frequently in fantasy and science fiction than in other genres. PJ Farmer's Wold Newton family works are one of the most famous examples of a shared universe concept.
In terms of Star Trek fandom a shared universe is generally one used by several authors, such as the Tetra-Luminaire Group (of which Star Trek: Liberty and The Adventures of Argus were members). Another prominent example is the United Trek universe, shared by several members of the TrekBBS. Shared universes are also employed by many online RPG groups, though not all members of a particular group may use the same setting.
Fan fiction authors sometimes also adapt material from television shows other than Star Trek. Often these are crossovers, where characters from one TV series or fandom "cross over" into the universe of another series. This is commonly seen in many "Star Trek vs. Star Wars" type stories, though the settings and characters used can go far beyond just those two universes.
Beyond crossovers, however, some authors create a truly shared universe between the fandoms. One popular variation on this type of shared universe is one where characters from Star Trek and Babylon 5 coexist without need for "crossing over." Such a universe can either depict Trek characters in a B5 setting or vice versa, or meld aspects of both universes into one (ie, where the Federation fought against the Shadows).
Star Trek: Unity (fan film series) is one such fan series that incorporates elements of Doctor Who, Stargate and Star Wars to flesh out its universe.