You mean how are companies like yahoo able to “create” domain names like yahoo.com?
If that’s the case, there’s a central authoritative database called the “Registry”. Just as there’s a registry for maintaining all authoritative registration records for, say, a state’s civil weddings, there’s one to manage all .com domain registrations.
The .com Registry is currently run by Verisign. Current contract stipulations prevent the Registry from doing domain registration themselves to prevent monopolizing and exploiting it.
The next best thing they can do, again based on their contract, is to “outsource” it (for lack of a better term) to certain companies who can continually meet stringent technical and financial requirements. These companies are called “registrars”, like Go Daddy, Network Solutions, etc.
When you register a domain name through Go Daddy, Go Daddy will create an entry within their computers and take your payment. In turn, they’ll forward a copy of your registration to the Verisign COM NET Registry (they also handle the Registry for .net domains) as a way of saying, “Hey guys, our customer registered this domain name. We’re sending you a copy of it for your records, okay?”
The capability to register domain names in computers is based on what’s called the Domain Name System (DNS for short). Because people tend to remember words instead of numbers (which is how computers “talk” to one another) when looking up information, certain technical professionals designed DNS to allow this.
Once the system was designed and “perfected” for easier use and management, the people in authority started writing contracts, finding and “accrediting” the right parties to handle them, and enforcing them to draw the lines as to what people can and can’t do. It’s a constant work in progress.