A domain is your private address on the internet.
You can build a website if you want, but for many people having a domain is a way of ensuring you never have to change your email again. If your email is currently something like your.name@yourISP.com.au and you change to a new ISP you will have to let everyone know your new email address.
However if you have a domain such as 123host.com.au and use that for your email address e.g. firstname.lastname@example.org, no matter who your ISP is, your email never changes as long as you keep your domain active and hosting alive. At 123host this is a relatively cheap service.