There has never been a canon explanation as to why the initials "NCC" are used or what they mean. It is known at the prefix "NX" refers to experimental ships.
According to Memory Alpha:
- "The use of "NCC" as a prefix for Starfleet registry numbers, Matt Jefferies said that the registries for American civil aircraft are preceded by "NC," and Soviet craft used a prefix of "CCCC," and as such, he more-or-less combined the two. His philosophy was, "If we do anything in space, we (Americans and Russians) have to do it together."
For more information, see MemoryAlpha, the Star Trek Wiki.
Whilst there is no official standing on the subject - some example (fan) definitions suggest that the CC initials correspond to "Constellation Class". Of course this must be purely coincidental since the NCC-1701D was a "Galaxy Class" design! The use of "NC" probably dates back to the first aircraft constructed jointly by the US Navy (N) and the Curtiss (C) Company... and the tradition has endured for nearly a century.