Having your own domain name means being able to use the same e-mail address or website URL for as long as you like.
Here’s how to register a domain name, get it set up for e-mail, and point it to another website. These instructions assume you’re using Namecheap; adjust them if you’re using something else.
When you’re done with the registration process, sign in again if you need to.
Then you can set up e-mail forwarding and URL forwarding if you like.
If you use Gmail to send mail, you can send mail using your new e-mail address in the From: field. Check out these instructions: Adding a custom ‘From’ address.
You can do more with domain names than what I’ve described here, but that might require some geeking out. =)