A post-game area in X and Y with boosted shiny odds.
The Friend Safari is a post-game area in X and Y. Each 3DS friend gives you a safari of one type, with Pokémon from many regions.
The game tries up to four extra shiny rolls for Friend Safari encounters. That is about 1 in 819, or about 1 in 585 with the Shiny Charm.
You may see "1 in 512" quoted elsewhere. Bulbapedia's Friend Safari page, which explains the roll math, gives the lower figure, so that is the one we use.