It hasn't been stated in canon, though it's commonly held to be "Naval Construction Contract" in non-canon works, and in fact this was planned to be canonized in Enterprise's 5th season before it was canceled. See here for a full treatment of the subject.
^^^ It should be interesting to note that Matt Jefferies (Star Trek TOS' Art Director, Production Designer and the reason why we have Jefferies Tubes) said that 'NCC' came to be when he combined the registry prefix for American aircraft (NC) with the prefix for Soviet aircraft (CCCC). His philosophy behind the decision was, quote: "If we do anything in space, we (Americans and Russians) have to do it together."
In contrast, the Star Trek Encyclopedia stated that the reason behind the 'NCC' prefix was more or less because of Rule of Cool. Make of that what you will. --Jonny hirst (talk) 11:31, July 27, 2015 (UTC)