Data in Mosets Tree is stored in 2 places. The database and the filesystem.

Images

/components/com_mtree/img/cats/
/components/com_mtree/img/listings/

The above 2 directories contains all uploaded images (both original and scaled version) for categories and listings. If you have any uploaded images in your directory, make sure you back up the 2 directories, including all its sub-categories and files.

Templates

/components/com_mtree/templates/

All templates are stored in the above directory in its own sub-category. Mosets Tree comes with a default template called m2 which is stored at /components/com_mtree/templates/m2/. If you did not modify the default template, you can skip this directory, otherwise, backup all files and directories in this template directory.

Language

/components/com_mtree/language/

This is where the language files are stored. Most directory has at least some modification to the language file, so backup this directory.

Database

Assuming your database is using the default database prefix, backup all tables that start with jos_mt_*. Most hosting provider provide an interface through phpMyAdmin for you to export the data in a SQL file. Make sure you export the data structures and the data itself.