Facebook email addresses are now being rolled out to the public... Although, at this time only certain accounts may still only be offered it, overtime you will be able to get it. Essentially, it's "yourusername@facebook.com" so the "@facebook.com" email address will match your public facebook username.
To find out if you can activate Facebook email, go to Messages in facebook and it will automatically ask you if you'd like to create a facebook email address.
To set up a free @facebook.com address, go to your Messages view and click the "Claim your Facebook email" link.
Your email address will match your public username, for example:
Profile: facebook.com/username
Email: username@facebook.com
If you don’t have a username yet, you can choose one when you create your email address.
Once you set up your email address, people can email you using any traditional email system (e.g., Hotmail, Yahoo or Gmail), and the emails will be delivered to your Facebook Messages. When you send messages to external email addresses, the emails will be formatted to look like Facebook messages, including your name, your profile picture and your message.