A domain name is a name used for a website such as “google.com”. You can purchase a domain name through a domain registrar who reserves this name with the central web administration such that you own that name and what servers that name points to.
If you don’t own a domain name, we recommend you purchase a Domain Registration through Google so that it will automatically setup a Google Apps account for you. Click here and then choose “I want to buy a domain name” on the right.
Your domain name is an address but it is separate from hosting which is what your domain name will point to, a server that will host your site.