From what I have read on this entry on the Pokemon Wiki about the Shiny Charm (Japanese: Hikaru Omamori, known as the Shiny Amulet), it is said that if you have this charm, it makes your chances rise a little bit to make it more likely to find a shiny Pokemon.
I think it's only obtainable in Pokemon X and Y and Pokemon Black & White (counting the sequels Black 2 & White 2) by completing the National Pokedex in the games.
It can be obtained from Prof. Juniper in Black & White/Black 2 & White 2 in Nuvema Town, and Prof. Sycamore in Lumiose City once the National Pokedex has been filled.
Here is what is looks like in the games. It may look the same in your Bag in Pokemon X and Y.
However, filling the National Pokedex all the way will be worth it, even though it takes forever.
I am aiming for this item, even though it will take forever for the National Pokedex to be completed in my game, Pokemon X.