A domain name gives you a unique address on the Internet - your digital signature, so to speak. Technically, a domain name is a way of connecting a name and an IP address. All computers connected to the Internet have their own unique IP address. To human beings, it is easier to remember names than digits, and hence a domain name system (DNS) has been invented allowing us to enter, for example www.domainnameshop.com (the domain name) instead of 126.96.36.199 (the IP address).
A domain name is registered for one or more years, and can be renewed as long as you wish to keep it. A short and describing domain name makes it easier for your customers and liasons to remember your email address or the address of your website. By having your own domain name, the address will remain the same, even though you choose for another provider to handle your email and/or your website.
A domain name is hierarchical structured, using comma-separation for different levels. domainnameshop.com is a top level domain, whilst www.domainnameshop.com and ftp.domainnameshop.com are sub domains of the top level domain. If you own the domain name example.com, you will automatically own all sub domains under this domain that you might want to create, e.g.
www.example.com, test.example.com and for.fun.example.com.