The Network Admin Themes Screen controls which themes are available to Site administrators in their Administration > Appearance > Themes Screen. Network Administrators must install the themes in the wp-content/themes folder for the themes to be available. Themes can also be selectively activated for individual Sites in the Theme Info section when Editing a site via Administration > Network Admin > Sites.
This table lists all of your categories by row. Categories are displayed hierarchically and alphabetically by the folder name used for storing that theme in the wp-contents/themes folder.
The table of themes contains the following columns:
When new sites are created via Administration > Network Admin > Sites, the WordPress Twenty Fifteen theme will be set as the active (default) theme. If a different active (default) theme is desired, edit the wp-config.php and add the WP_DEFAULT_THEME constant definition to the file. For example to make the WordPress Classic Theme the default theme put this in wp-config.php:
If you do remove the WordPress Twenty Fifteen theme then you need to define a new default theme with the WP_DEFAULT_THEME constant. Disabling a theme in the Network Admin Themes Screen does not prevent that theme being used by a site. It only prevents the theme being listed in the available themes list when selecting a new/different theme.