All information stored as web sites on the internet is hosted on servers.
A server is a computer or a computer system which stores the information of the web sites it is hosting (storing & distributing) on its hard drives.
The server has a connection to the internet and like people having a telephone number a server has an IP address. An IP address is a number like 123.456.78.9. It is now not so nice if people have to only deal with numbers to reach websites. A real name like mydomain.com.au is easier to be remembered than a number. So you can go to a Domain Name Registrar and register a Domain Name. At the Registrar's web page you type in the domain name you would like to register and their system tells you if the domain is available. The last letters of the domain on the right side like .com or .de or .com.au are called a Top Level Domain (TLD). Even if your desired domain name might not be available - like mydomain.com - it might be available for mydomain.com.au . After you registered your domain name at the registrar you have to tell the registrar the location where your website is hosted. This is done by entering the name servers (like ns1.tekwizard.prodns.net.au) in a page at the domain registrar. The registar will distribute the new address associated with your Domain Name to a list of Domain Name Servers (DNS). A Domain Name Server or DNS works like a phone book, so that the IP address of your server hosting your web site is properly associated with your Domain Name.
So to say it in a few words: you need a domain name so that your website can be found.