Which means that you have to provide to the plugin the paths to mysqldump and mysql on your local server. The Auto Detect buttons not always can help. So I had to search for the two files into the MAMP Library. And in case you had a hard time finding them as well, here you have it.
Path To mysqldump:
Path To mysql:
Just copy and past the paths as they are into the corresponding fields on the DB Options page for WP-DBManager. Done that, you should be able to backup your database.