So the best way to backup your mails from Thunderbird is to copy your complete profile directory. Follow these steps for restoring your mail.
The fool that I am, instead of copying the full profile directory I ended up backing up just the Mail subdirectory in the profile directory. It took me a while to figure out how to restore the backup, so I thought I would share it with you.
The first thing you do is install Thunderbird (if you haven't already). Now Run( Windows : Start->Run or press Win key+r ; Mac/Linux - you're smart enough to know :P ) this command "thunderbird.exe -profilemanager". Create a dummy profile - just have some dummy email address in there. Now exit Thunderbird.
Next step is to find your newly created profile directory. Locate the Mail directory in there. Now you have to copy 2 files from your backup - both have the same name. One has a .msf extension and the other has no extension. I had created a separate thunderbird mail folder with a filter and I needed to backup just that one alone. So I just copied those 2 files (from the Inbox.sbd directory) and put them in the Local Folders subdirectory in the Mail directory (which already had empty files like Trash and Trash.msf).
The file without extension - this is the actual mail file. It's in the mbox format. The other is an index file.
Acknowledgements :
I posted a question on Aardvark - http://vark.com/t/eee11d. I got replies from Shel and Moez. I would like to thank both of them for helping me out.