Help screen column header Contact Category Permissions
From Joomla! Documentation
The permissions section for the category will be at the bottom of the screen and will look like the following:
The options allowed are:
Create new items in the category
Delete existing items in the category
Edit existing items in the category
Change an items state (Publish, Unpublish, Archive, and Trash) in the category.
Edit existing items in the category that the logged in user has created.
There are two very important points to understand from this screen. The first is to see how the permissions can be inherited from the parent Group. The second is to see how you can control the default permissions by Group and by Action.
This provides a lot of flexibility. For example, if you wanted Shop Suppliers to be able to have the ability to create an item in the category, you could just change their Create value to "Allowed". If you wanted to not allow members of Administrator group to delete objects or change their state, you would change their permissions in these columns to Inherited (or Denied).
It is also important to understand that the ability to have child groups is completely optional. It allows you to save some time when setting up new groups. However, if you like, you can set up all groups to have Public as the parent and not inherit any permissions from a parent group.