A NOC (No objection certificate) is certificate which shows clearance of a subject. For example, your buying the desired vehicle of your choice and you have to prove that the vehicle your buying hasn't been stolen, the taxes and tokens have been paided, the vehicle is clear of all government dues whatsoever and it's CPLC is cleared.
In short, it's basically proof to the government that the vehicle your purchasing is cleared, and has no dues or formalities to be done upon it.