Assuming Windows:

BACKUP

1. ensure thunderbird is not running
2. enter %appdata% in search window on task bar and press Enter key
3. this should open windows file explorer in Appdata\roaming folder
4. highlight the Thunderbird folder and copy to external media

RESTORE

1. ensure thunderbird is installed and NOT running
2. enter %appdata% in search window on task bar and press Enter key
3. you should be in Appdata\roaming folder , copy&paste the exported Thunderbird folder there. This will prompt to overwrite an existing folder of same name. allow it
4. start thunderbird and all should be there

I copied this information to my computer, thanks!

Question - Is it possible to backup ONLY the email messages?

Yes, you can do that, but it's a tad more complex. If the messages are in a POP account, they are already safe on your PC. If they are in an IMAP account, they usually are, but confirmation is needed. Here are suggested steps/

1. first, install the addon, importexporttools NG
2. For POP messages, highlight the folder, rightclick and select the importexport option to export mbox (if you want to save the folder for later use within thunderbird) or export EML (if you want to save the messages as individual email messages).
3. For IMAP messages, highlight the folder, rightclick and select importexport option to export mbox. Then, highlight Local Folders, rightclick and select importexport option to import mbox and import the file you just exported, If the folder has all your messages, then now follow the same instructions as for POP.

The process is much easier than it looks. Honest. :) Let me know if you encounter problems