Understand that 'appurtenance' often refers to items that enhance the main object but are not essential. A detachable camera lens is an appurtenance to the photographer's equipment.
Pro Tip 2/3
Not Standalone
'Appurtenance' implies dependency; it doesn't make sense without the main item it's associated with. A pool is an enjoyable appurtenance to a house, not a structure on its own.
Pro Tip 3/3
Enhanced Value
Appurtenances are meant to increase the value or functionality of the item they accompany. The smartphone case with a built-in battery is a valuable appurtenance.