One of the greatest things about the Internet is that nobody really owns it. It is a global collection of networks, both big and small, that connect together in many different ways to form the single entity that we know as "the Internet." Since its beginning in 1969, the Internet has grown from four host computer systems to tens of millions. However, just because nobody owns the Internet, it doesn't mean it is not monitored and maintained in different ways. The Internet Society, a non-profit group established in 1992, oversees the formation of the policies and protocols that define how we use and interact with the Internet.
When the Internet was in its infancy, you could only make connections by providing the IP (Internet Protocol) address of the computer you wanted to establish a link with. For example, a typical IP address might be 188.8.131.52. This was fine when there were only a few hosts out there, but it became very unwieldy as more and more systems came online. The first solution to the problem was a simple text file maintained by the Network Information Center that mapped names to IP addresses. Soon this text file became so large it was too cumbersome to manage. In 1983, the University of Wisconsin created the Domain Name System (DNS), which maps text names to IP addresses. This way you only need to remember www.howstuffworks.com, for example, instead of 184.108.40.206.
The Domain Name System is a distributed database, but there are central name servers at the core of the system (see How DNS Works for details). Someone has to maintain these central name servers to avoid conflicts and duplication.
In 1993, the U.S. Department of Commerce, in conjunction with several public and private entities, created InterNIC to maintain a central database that contains all the registered domain names and the associated IP addresses in the U.S. (other countries maintain their own NICs (Network Information Centers) -- there's a link below that discusses Canada's system, for example). Network Solutions, a member of InterNIC, was chosen to administer and maintain the growing number of Internet domain names and IP addresses. This central database is copied to Top Level Domain (TLD) servers around the world and creates the primary routing tables used by every computer that connects to the Internet.
Until recently, Network Solutions was the only company that provided domain names. However, to ensure that Network Solutions did not become a monopoly, the U.S. government decided that other companies should also be allowed to sell domain names. While these other companies (known as registrars) provide domain names and maintain DNS servers, Network Solutions still maintains the central database to ensure that there are no duplicates. In the U.S., you pay Network Solutions an annual fee to maintain your domain name in the central name server.
The following links are helpful: