Mozilla thunderbird stores your email and profile setting in a special directory called ~/.mozilla-thunderbird i.e. /home/you/.mozilla-thunderbird/. All you have to do is backup this directory.

Task: Backup Thunderbird mail and profile

You need to backup thunderbird mail and profile to tape drive, use:       

            # tar zcvf /dev/st0 /home/you/.mozilla-thunderbird/

You need to backup thunderbird mail and profile to a /backup directory: