Phantom membranes are obtained by killing phantoms, which spawn if a player has not slept for three in-game days. They cannot be crafted but are a renewable resource through phantom farming.
Phantom membranes are primarily used to brew Potions of Slow Falling, which reduce fall damage and extend mid-air control. They are also required to repair elytra in an anvil, making them essential for elytra durability and flight maintenance.