A domain name is a two part name that identifies a site or area on the internet to the rest of the world.
Many businesses like to have a domain name to identify themselves easily for their customers.
You have to register the domain name with an official registering body. There used to be just one place to do this, the internic. NOT all of them cost the same, either, so shopping around is a good bet. In registering a domain name, you have to search to see if it's available or not. All the registering places have areas where you type in what you want and it will tell you if the name is available.