This page works exactly the same was as WordPress tags, so if you’re not sure about how it works, you can check the WordPress documentation.
Here is the Genres Taxonomy page. The pages for series, tags, editors, illustrators, and cover artists works exactly the same way. On this page you can add a new genre by filling in the fields and pressing the Add New Genre button. Or you can edit an existing genre by selecting on from the list on the right.
The Description field is not used by Mooberry Book Manager, however your theme may or may not use it.
If you have WordPress version 4.4 and above, you will see two fields on this page: Book Grid Description and Book Grid Description (Bottom). These fields allow you to set text to display above and below the Taxonomy Book Grid for the selected item. Each item in the taxonomy can have its own Book Grid Description, so, for example, you can have different text for your Contemporary Genre Taxonomy Book Grid and Historical Genre Taxonomy Book Grid.