If you have made a back up of your Thunderbird files in the Unix-based tarball (.tgz) file format, then you cannot import directly from that format. Instead you will have to extract the data from your tarball in the first place and then import the content that is stored in that file. Tarballs are single file archives that store and compress other selections of data.
Open the terminal and change the folder to your tarball directory.
Type "tar xzvf tarball.tgz" replacing "tarball" with the tarball file. Press "Enter" and close the terminal.
Open Thunderbird, click "Tools," then "Import." Choose the type of import you want to do, select the data from the tarball and click "Import."