Basically it just means that if an ally that is in a nearby slot dies, it gets sent back to its owner's hand and the Djinn gets sent back to the lamp.
If there is no lamp for the Djinn to go to, the Djinn dies.
That means you can summon them from your hand, but they basically sacrifice themselves to save others if there aren't enough lamps in play.
Whenever a lamp is destroyed, whatever Djinn came from it is also killed.