Hi,
first of all, Address Book is an application of its own. It's not just a sidecar for Mail. A lot of other applications use it, too.
How Mail uses Address Book.
Composing a new message
Start typing away the name (e.g. John) and it will look up all email addresses of John, stored in your Address Book, presenting you the real name and the email address.
If you have groups in Address Book (e.g. for a team you're working on, you sports team, etc.) you can put in that group name into the "To" field of a new Mail message --> all the email addresses of that group will get inserted.
In Address Book
You can also use Address Book as the starting point. Control-clicking the various fields, reveals options for stuff you can do with the data (read: if you click on an email address, you can compose a message, if you click on a phone number, you can dial it with Skype, if you click on a mail address, you can look it up in Google Maps).
Other Applications
As said before a lot of applications support to get an address, phone number or any contact information from Address Book.
Skype, for example, can display all contacts with a phone number on your Skype buddy, so you can call them with the cheap SkypeOut.
Synchronization
Moreover, you can synchronize your contacts with your bluetooth-enabled mobile phone. I wrote a tutorial on how to set this up, over at
Mac Kindergarten.
Hope this was helpful.
/Rupert