If held by a Latios, the Latiosite allows it to Mega Evolve into Mega Latios 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 Latiosite from Latios.
Outside of battle
If held by a Latios, the Latiosite allows it to Mega Evolve into Mega Latios when it performs a Spectacular Talent during a Pokémon Contest Spectacular if its Trainer has a Key Stone. Latios will remain a Mega Latios until the Talent Round ends.
Data for Latiosite and Latiasite exists within the code of Pokémon X and Y, despite the Mega Stones not being officially introduced until Omega Ruby and Alpha Sapphire, which allows them to be transferred to and used in X and Y.