(covers information from several alternate timelines)
USS or U.S.S. was a prefix used before the names of some sea-faring ships and spacecraft. The abbreviation has been used to stand for "United States Ship", "United Space Ship" and "United Star Ship". The prefix was first used on Earth by the United States. Its use has been continued by the United Earth and the United Federation of Planets.
As shorthand for "United States Ship," the US Navy used the USS prefix on the hulls of various sea ships and aircraft carriers, including: USS Enterprise (CV-6), USS Enterprise (CVN-65) and USS Monitor. (ENT: "Storm Front"; Star Trek IV: The Voyage Home; TOS: "The Cage")
Starfleet used the "USS" designation on certain computer graphics for United Earth NX-class starships, such as the Enterprise NX-01 and the Columbia NX-02. However, they did not label the hulls of the starships and the ships were not commonly addressed with the prefix. (ENT: "Divergence")
On Federation starships operated by Starfleet, the "USS" prefix was more prominently featured on the hull of the ship and as part of the starship's official title. USS was referred to stand for either "United Space Ship" (TOS: "The Cage", "The Menagerie, Part I", "Space Seed", "The Gamesters of Triskelion", "Patterns of Force", and more) or "United Star Ship." (TOS: "The Squire of Gothos", "Court Martial") This designation was used as early as 2167 on the Daedalus-class starship, the USS Essex. (TNG: "Power Play")
The first spaceship from Earth known to use USS was first shown in Star Trek: The Motion Picture in the picture of the USS Enterprise (XCV 330) on display in the recreation deck of the refitted USS Enterprise (NCC-1701). The placement of a desktop model of this craft in Star Trek Into Darkness suggests the ship predates United Earth, so the USS designation may have still meant "United States Ship" at that point in history.
Shortly before Star Trek: Enterprise began its initial airing, Rick Berman implied that Enterprise NX-01 was purposefully without the "USS" prefix because it wasn't a Federation starship. (Star Trek: Communicator issue 134, p. 13) The use of USS by Starfleet before the formation of the Federation was only seen on a computer graphic in the Enterprise episode "Divergence". This graphic had both the Enterprise and the Columbia designated with the USS prefix, which may have been a mistake on the part of the graphics designers, as neither ships' hull designation used "USS".