Authorizations (as they're called in J1 Desktop and the campus portal) are called Overrides in J1 Web.
If this checkbox on the Web subtab of the Courses tab in the Courses window is selected, students are able to register for the course online only after the instructor or personnel from the Registrar’s Office has granted an authorization or override.
Faculty use the Course Overrides page from the J1 Web Faculty hub, selecting the Registration Permission Required (P)" type.
Faculty use the Course Authorizations feature in the campus portal, selecting the “Course Capacity (C)” type.
For granting this kind of override in J1 Web, the instructor needs "Can grant registration permission required overrides" permission on the Registration Administration hub | Roles page. The permission is available (but deselected by default) in faculty, registrar, department head, and course information roles.
For granting this kind of Authorization using the campus portal, the instructor needs Override Course Authorization Required for Registration Errors" permission on the CRM Module Permissions tab of the Registration Permissions window.