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The Federation universe was a parallel universe where Earth was part of the United Federation of Planets meta-government in the 23rd and 24th centuries.
History
This universe was joined together with the Doctor's universe by the Cybermen so that they could form an alliance with the Borg, a similar cybernetic race native to this universe. The only known people who were aware of the two universes having been merged were the Eleventh Doctor and Guinan. (COMIC: Assimilation²)
Overview
While the planet Earth and humans existed in both universes, some of the races native to the Federation universe were not known to exist in the Doctor's universe, including the Borg, the Klingons, the Vulcans and the Deltans. Aside from the Federation itself, major powers included the Klingon Empire and the Borg Collective.
Behind the scenes
This universe is the setting of the Star Trek franchise and appears in relation to Doctor Who only in the Assimilation² cross-over comic.