Clicking the 'categories' link next to a group takes you to the Edit Group Categories page:

Here you can specify which categories users in this group can edit. When ticked, users in this group will be able to add and edit sub-categories of the selected category (ie. they will not be able to edit or delete the category itself). 

Once a user group has permission to edit a category, users in this group will see an Admin section in the left hand menu containing a link to the Categories admin page: