If you are wanting people to remember your web site address you are going to need to make it easy to remember.

This is where a "Domain Name" comes in very handy.
Instead of a web address like "http://home.visualimpressions.co.nz/~personal/yourname" which can be quite a mouth full to remember you can have a catchy name like "www.me.com".

I am sure you will agree people are more likely to remember a name that is short and catchy than long and complicated.

If you want some useless information:
If you have a domain name for you site, the server that picks up that some one has entered "www.me.com" then in the background where no one can see it just redirects them to "http://home.visualimpressions.co.nz/~personal/yourname" where your pages are really located.

This is not necessary that you have a domain name but if you choose to then it can be included in your web packge.