It is said to be the place where Celebi once landed, and so had the power to let Shadow Pokémon remember their happy and carefree lives before the doors to their hearts had been closed. Visiting the Stone would let them relive their memories and revert to normal Pokémon once again.
In Pokémon Colosseum, if a Time Flute is used at the Relic Stone, Celebi will appear and purify one Pokémon even if its Heart Gauge is not empty.