Mail is a part of OS X, it is a dedicated email program that can handle POP, IMAP, and Exchange services. You can use it for your gmail and other accounts. If you want a dot mac account (bellevue@mac.com) you need to sign up for that here: http://mac.com
The @mac.com email addresses are part of the dot-mac suite of services. It's $99 a year, and the various pros and cons of the service can easily be found debated throughout these forums ad nauseum.
Once you get in (which you will), buy a license off of eBay if you want to join. Just search "dotmac" and you will find them. Get it from a highly rated seller and you will get it at a good discount.