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.
There is a small chance that Eagun will win his cutscene battle against Skrub, only achievable if Hitmontop is paralyzed by Pikachu's Static and gets repeatedly immobilized as a result. However, this is not reflected in the following cutscene, which will still depict Eagun having lost.