USS is used in the United States Navy as a shorthand for "United States Ship." However, in "Star Trek," USS took on an entirely new meaning, thanks to creator Gene Roddenberry.
In "Star Trek," Starfleet gives space ships USS designations, but the meaning has changed several centuries into the future to mean "United Space Ship" or "United Star Ship."
Roddenberry fought executives over this change, as explained in the reference book, "The Making of Star Trek" by Stephen Whitfield. NBC executives had other plans.
They wanted the Enterprise to be a "good, safe patriotic United States spaceship." However, affiliating the ships with the U.S. would've been uncharacteristically nationalistic.