SemperWiFi's instructions are great for moving to Outlook, but I read you as saying you'd like to copy your email from one Thunderbird installation to another Thunderbird installation. It's actually almost too simple; you don't need to use an Import function.
If you look at the Server Settings for your account (Tools menu, Account Settings, then in the list on the left, move down one item to Server Settings), you'll see "Local directory". You want to move all the files from this Local Directory of the old Thunderbird installation to the Local Directory of the new Thunderbird installation. Each of your mail folders is represented by two files: one has no file extension at all, and contains the actual emails, while the other has a .msf extension, and is the index to the other file. Copy the files over while TBird is shut down on both machines. You'll need to rename files like Inbox and Sent which are in both locations; make sure you rename both the email file and the .msf index file. Skip copying any other files that are duplicates between the two locations.
When you restart TBird on the new computer, it will read all the mail files in the directory and list everything in your folder list. You're done!
