This Key Item increases the likelihood that you will encounter Shiny Pokémon. When you have the item in your bag, then the chances of encountering Shiny Pokémon in the wild is increased to 300% of normal, making it a 1 in 2,730.6 chance. If, however, you're using the Masuda Method to breed, it increased it from 1 in 1,365.3 down to 1 in 1024.
As of Pokémon X & Y, the rate increases from the standard 1 in 4096 to 1 in 1365.3
This is the exact test from Seribii about what it does.