Domain names serve as humanly memorable names for Internet participants, like computers, networks, and services. Your website for an example needs a domain name because it is hosted on a web server that has an IP address which identifies it with/from the rest of the internet. Without this technology people would be stuck typing in IP addresses to access their favorite websites. In a nutshell a domain name is the human helper for connecting us with IP addresses by having to type the actual name instead of a series of complicated numbers.
Examples of domains include google.com, yahoo.com, completehostingguide.com and whitehouse.gov.
You should decide on choosing a domain name with some sort of planning, thought/thinking, and feelings. After all it is your website name and the name you will own for at least one year. Make it something that describes you, your business or the idea, message or story you are trying to get across. A great example of a great domain name would be CompleteHostingGuide.com. But we're a little biased. ;)