Whenever you see "www.yourbiz.com", you are looking at a Domain Name. You can lease a Domain Name for your web site for approximately $35 per year. Acquiring a Domain Name gives you an official Internet name you can use for your web site, but until you acquire web hosting and construct a web site, the name is meaningless. That is, until you have a physical Internet address established, the Domain Name doesn't really point to anything.
You can get a Domain Name from a registrar such as Network Solutions, or, commonly, get one when you purchase a web hosting plan from a web hosting vendor.
You can purchase as many Domain Names as you wish - some people buy every possible name related to their business, including commonly misspelled terms! For marketing purposes, it is generally preferable to buy names reflecting your products or services and NOT your business name.