(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Tranquility Base was a location on Luna, part of Mare Tranquillitatis ("the Sea of Tranquility"). In 1969, the area was the site of the first Human moon landing by Apollo 11's Lunar Module Eagle. (TOS: "Tomorrow is Yesterday")
In the mirror universe, in the mid-2250s, the ISS Discovery was commissioned at this universe's equivalent of the base. The base was mentioned on the ship's dedication plaque. (DIS: "Despite Yourself")