Pause or activate a link with the toggle in the Status column of your dashboard (or from the edit page). A paused link stops redirecting until you switch it back on. Pausing does not free up a plan slot.
Delete a link with the bin icon. This is permanent: the path stops working and the link's stats are gone. Deleting frees a slot on your plan.
If a link should only be down temporarily, pause it rather than deleting, so you keep the URL and its history.