If held by a Mewtwo (or is present in the player's BagPE), the Mewtwonite Y allows it to Mega Evolve into Mega Mewtwo Y if its Trainer has a Key Stone. A Trainer can only Mega Evolve one Pokémon per battle (or only have one Mega-Evolved Pokémon at any given momentZA).
As a Mega Stone, it is unaffected by item-negating effects (such as Embargo and Klutz). Item-manipulating effects (such as Trick and Fling) cannot give or remove a Mewtwonite Y from Mewtwo.
Outside of battle
If held by a Mewtwo, the Mewtwonite Y allows it to Mega Evolve into Mega Mewtwo Y when it performs a Spectacular Talent during a Pokémon Contest Spectacular if its Trainer has a Key Stone. Mewtwo will remain a Mega Mewtwo Y until the Talent Round ends.
A Mewtwonite X and a Mewtwonite Y appeared in The Discovery, under Green's possession. After discovering that Elaine had managed to catch Mewtwo before her and being defeated in battle by her, Green gave the Mega Stones to her.
In Mewtwo Angered, Blaine was revealed to be in possession of both a Mewtwonite X and a Mewtwonite Y, which he can use to Mega Evolve Mewtwo. After Mewtwo's Mega Evolution into Mega Mewtwo Y was undone while battling Lysandre and Zygarde, Blaine swapped its held Mega Stone, allowing Mewtwo to Mega Evolve into Mega Mewtwo X and keep on fighting. Blaine then explained that due to the unique bond he and Mewtwo share, Mewtwo is able to Mega Evolve more than once per battle.