Why is the Resurrection Stone important in Harry Potter and the Deathly Hallows? What are its qualities?

In Harry Potter and the Deathly Hallows, the Resurrection Stone is one of the three deathly hallows. It was given to Cadmus Peverell, allegedly by Death himself, though Albus Dumbledore believes the stone was created by Cadmus himself. Cadmus used the stone to bring back a woman he loved, but he felt he was still too separated from her and killed himself to be with her. The ring containing the stone is eventually passed down to Albus Dumbledore and then to Harry Potter, who uses the stone to see the shades of his parents. 
The stone is important because its owner has the power to bring back shades of loved ones. Shades are figments of people that are more substantial than ghosts but less substantial than real people. If someone brings the Resurrection Stone together with the other hallows—the Cloak of Invisibility and the Elder Wand—the person who possesses all three hallows will become the Master of Death.