FileZilla itself does not provide functionality to unzip files on server. So here comes a handy solution using PHP.
Navigate to your directory where the zip folder is
Here create a file unzip.php
Now edit this file and write
<?php system('unzip your_zip_folder_name.zip'); ?>Next in browser visit this file for example
http://mysite.com/unzip.php
and done. Zip folder will be unzipped.