NCCNCC is an imaginary designation for starships conceived within Star Trek. According to Star Trek chronology, the term was first used in the Original Series. It has been suggested that the prefix "NCC" was used by the creators of Star Trek as a combination of a United States Naval prefix "NS" ("Naval Ship"), and the Soviet Union acronym "CCCP" to show that the two countries had to work together to establish Starfleet. Another more popular theory is that it derives from the 'NC' prefix used for United States airplanes - creator Gene Roddenberry was a pilot.
In the original series of Star Trek, the only registries seen were for ships either unseen, or seen to be of the same class as the Enterprise. The speculation by fans as the time was that 'NCC' was a hull code like the United States Navy's codes, which designates the basic types of vessel, and is then followed by a ship identifier number. 'NCC' was explained as 'cruiser' and 'NDD' suggested as a 'destroyer'.
This was blown out of the water by Star Trek II: The Wrath of Khan, which featured the USS Reliant, a clearly inferior ship to the Enterprise, and still registered under NCC.
Later films and series showed that nearly all Starfleet ships used 'NCC', but a few, experimental ones used 'NX' (seen on the Excelsior, and Defiant).
This was confirmed in Enterprise with the registry 'NX-01' for the experimental ship of the title, but this was explained in a way which is at odds with chronologically later usage - NX is being used as a class name, and 'NX-01' means 'the first ship of the NX class'. It remains to be seen how or if these systems can be reconciled.