Network Information Center. There have been several meanings for this, starting from the central repository of contact data, domain names, IP addresses and parameter protocolos.
Used in many countries to refer to what we now call a ccTLD manager. Examples: NIC MX for NIC Mexico (see http://nic.mx). Many users expect to find the central website for a TLD (ccTLD or gTLD but mostly the first) at http://nic.<code for the gTLD> and also to be able to send email to addresses at that domain name.