The Masuda method, also known as Masuda's method (Japanese: 国際結婚 international marriage), is a fan-made term which describes a way to obtain Shiny Pokémon more easily in Generation IV and V. Rather than encountering Shiny Pokémon with a probability of 1/8192, the Masuda method lets players breed Pokémon of differing real-world geographical origin with a 1/1639 (Generation IV) or 1/1366 (Generation V) probability of being Shiny upon hatching.
And how to do it:
The key to using the Masuda method is not to breed any two Pokémon, but to breed two Pokémon created in games of different countries. An Egg resulting from such a pairing will have a higher likelihood of being Shiny. The most common way to arrange such a pairing is to use one foreign Pokémon and one from the game in which the breeding occurs, although the method will work in any game provided at least one of the Pokémon in the pair is from a country different to the country of the game cartridge.
If both Pokémon are foreign to the cartridge but are both from the same country, then the Masuda method will not take effect. Foreign language Pokémon obtained via in-game trades, such as the Meister's Foppa and Lt. Surge's Volty, are treated as being from the same country as the game, because they are generated in the same cartridge, so they cannot be bred with another Pokémon from the same country for the Masuda method. In Generation IV, if the Masuda method is in effect, so both parents come from different countries, the Everstone will fail to increase the chance of passing on a nature.
In simpler terms, breed 2 foriegn Pokemon together to get a higher chance with hatching Shinies.