A domain name is a name, such as microsoft.com, yahoo.com, or MyServer.org, which uniquely identifies your company, product, service, industry or interests.
They can be used for web sites and personal e-mail addresses (such as you@yourcompany.com). The machines on the Internet only understand addresses in numerical form, for example 68.15.187.28, so a domain name is used to make the address easier to understand.
The above address might point to MyServer.org where "MyServer" is the name of the company, and "org" is the part of the global network on which the machine sits.