A domain name is an address to access a site on the World Wide Web.  There are various levels of domain names, for example top level domain names such as .com or .org or country level domain names such as .co.uk or .tv.  The top level domain names are regulated by a body called Verisign, and the country level domain names are regulated by national registries.  In the UK, the national registry is called Nominet.  National registries have their own regulations (e.g. in certain countries a company registration for an identical name to the domain name is required before registration of the domain name can take place).  

It is important to note that owning a registered trade mark does not provide you with an automatic right to the domain name.  It is also important to note that use of a domain name can infringe the rights of a third party which owns a registered trade mark for an identical or similar mark to the domain name.

Links: Domain Names