"Then the second brother, who was an arrogant man, decided he wanted to humiliate Death still further, and asked for the power to recall others from Death. So Death picked up a stone from the riverbank and gave it to the second brother, and told him the stone would have the power to bring back the dead."

The Resurrection Stone was one of the three Deathly Hallows, originally in the possession of Cadmus Peverell. In layman's terms, it gave its owner the power to bring back a form of the dead. To be specific, when the Resurrection Stone is flipped over three times in one's hand, it brings back shades of the holder's deceased loved ones as long as the stone is held. These shades are more physically solid than a ghost, but less so than a living body. Aside from this power, when the Resurrection Stone is owned in conjunction with the other two Hallows, it makes the owner the Master of Death.