Polished Black Stones have roots in ancient religions, alchemy, early medicine, and science.
In religion, The Black Stone dates back to Abraham, "The Kaaba was built by Ibrahim (Abraham) and his son Ismail (Ishmael) on the foundations of an older Kaaba." The Black Stone occupied the eastern corner.
In alchemy, they represent initiation and transmutation of the alchemists. They were also used during readings by prophets, seers, and shamans.
Stones have long been used in Asia for magnetic massage therapy. By walking on them they act as Acupressure stones and they channel the built up magnetic charge in the body to the ground.
Magnetic lode stones have long been used for many earth science applications.
In the movie, the stones represent a "pass" or "invitation" to be delivered from the Earth's annihilation.