Generally this refers to the name of the computer (or more specifically, the server) connected to the Internet. However, there are cases where a domain may map to more than one IP address.
As no two domain names may be the same, no two persons or groups may hold the same name. Once a group or person registers a domain, they have exclusive rights to it over a specified period of time. As long as they continue to renew the domain name and pay the renewal fees, no-one else will be able to use their domain. Consequently, domains are being registered at a rapid rate as businesses fall over each other to get on the Net. This also led to some scam artists quickly registering domains they knew would be registered by companies later on, and proceeding to sell the domain names to the companies at great profit.

(see DNS).