What does the prefix "NCC" on a starship mean?

Interesting question...there are several answers found on the internet:

• Star Trek Wikia says: 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- 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- this is pretty consistent with Gene Roddenberry's answer (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.

• The Star Trek Encyclopedia says: 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."

• According to non-cannon sources: "NCC" is short for "Naval Construction Code", "Navigational Contact Code" or "Naval Construction Contract" (Star Trek Starfleet Technical Manual. New York: Ballantine Books (1975). ISBN 0-345-34074).

• Another possible explanation for the "NCC" registry code comes from 20th century US Navy Hull classifications. "CC" was the classification for a Heavy Cruiser during Gene Roddenberry's stint in the Navy. The "N" would imply that the Cruiser is nuclear powered. This explanation would account for the Enterprise, but is unacceptable for explaining many of the other ships shown in the motion pictures and subsequent series, which would have used other designations (CV=Aircraft Carrier, BB=battleship, etc.)