The checkbox for "Hide the add shortcut link in structure" defines the visibility of the "add shortcut" link that is visible in structure below the list to the left (in the standard forms3 list interface).

If you check that checkbox, the "add shortcut" link will not be displayed for any user. This is useful for platforms where the assignment into folders is mostly done in a different way, as means not to distract users and to avoid misunderstandings.