A Black Stone was the symbol that someone had been chosen to be one of the seven tributes to the Minotaur in the Labyrinth and sacrificed so the the city of Atlantis would be safe.
The stones were drawn in front of King Minos and Queen Pasiphae from the mouth of a hollow bull statue. A white stone meant you were safe, a black stone meant you were to be a tribute to the Minotaur. The chosen people brought their black stones to the palace the day after picking them and were taken to the Labyrinth by some of the city guards. Pythagoras was unlucky to pick the black stone, but Jason decided to take the responsibility upon himself. (The Earth Bull)