Unconnected links represent a service that is not connected to some other host, for instance an unused interface on a router. They are drawn as short lines extending out from the host. The first unconnected interface is drawn straight up ("12 noon") and the rest are evenly distributed around the host in a clockwise fashion. You can choose to display or not display the unconnected links.
As these unconnected links show any service for which the device has an active monitor, you can use this feature to show a visual status of the services. For example, though the device is up (green), you may see that one of the unconnected links is down (red) and will know to check the services on the device.