According to Arabian folklore, a genie's lamp held a magical spirit (a djinn or genie) which could help or hinder those who encountered it. The best known tale involving a genie lamp is that of Aladdin, who rubbed the lamp to summon the genie and grant him wishes.
Genie lamps often appeared quite ordinary in stories, suggesting that true power often lies in unlikely locations.
Like angels, genies represent beings which exist beyond our realm of perception. Genie lamps thus signify a connection between the normal world and a greater universe of which we might not be aware.
Stories such as Aladdin depict genies as being inhumanly powerful--able to conjure castles out of thin air or remove the moon from its orbit--which grants the lamp an equal sense of power or strength.
When wishing to a genie, characters traditionally took care to voice their wishes precisely, or else the genie may interpret them too literally. Hence, genie lamps represent the dangers of power as well as the benefits.
In Western tradition, genie lamps usually grant three wishes: suggesting that power, once attained, is still limited and must be used with care.