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: