A Domain Name is the portion of a URL that is unique to a web site. For the URL "http://www.MichaelHaynes.com", the Domain Name is "MichaelHaynes.com".
Each Domain Name is registered to only one owner via a Domain Name registrar. Registrations expire after a pre-specified period of time, and must be re-registered beforehand (with any registrar), otherwise another could register the same Domain Name, and thereby obtain rights in that Domain Name.
Disputes can arise when someone registers a Domain Name that is confusingly similar to another's Domain Name, or to another's Mark, particularly if the Mark is famous.
The ICANN organization has promulgated a Domain Name Dispute Resolution Policy with which most registrars comply.