The Starfleet starship registry prefix "NCC" doesn't officially mean anything other than it is the standard prefix for starships in service. There have been other prefixes, notably "NX," denoting a prototype, or experimental vessel* (see footnote below).

When Star Trek creator Gene Roddenberry was asked this question, he replied that there was no significance to the letters and numbers comprising the registry of the U.S.S. Enterprise. At the time Star Trek first aired, airplanes commonly had "NC" on them, and adding the extra "C" updated the look.

Original series art director (and avid pilot) Matt Jefferies commented that he chose the "1701" combination of numbers because it was legible from a distance and the numbers wouldn't be confused. Other numbers, like 3, 2 and 5, were not used for this very reason. Also, the extra "C" in "NCC" was a nod to the Russian abbreviation for the old Soviet Union, "CCCP." According to Jefferies, "If we do anything in space, we (Americans and Russians) have to do it together."

*Prior to Star Trek: Enterprise, the two most famous ships with the "NX" prefix were the U.S.S. Excelsior NX-2000 and the U.S.S. Defiant NX-74205. Once the U.S.S. Excelsior was rendered operational, the prefix changed to the standard "NCC."

In Star Trek: Enterprise, however, Captain Archer's Warp 5 flagship was designated the NX-01, and its sister ship, the Columbia, was NX-02. Archer once referred to that style of starship as "NX-class." Whether or not "NX" was intended to indicate prototype status in the 22nd century is unclear.