In the games, trainers have a unique ID number that helps distinguish them from other players. This number can be found on the Game Boy cartridge and is used for various things, like trading and battling.
The Meowth in Pokémon Mansion is a bit of a con artist and will try to scam trainers out of their "diamonds" (ID numbers) by claiming he can use them to find a rare Pokémon. Of course, this is a lie, and he's just trying to get your ID number so he can use it to get a free pass to the mansion.
So, the next time you see that Meowth in the mansion, don't fall for his tricks! Just remember that he's only after your "diamond" (ID number).