Breeding two Pokémon from different-language games for better shiny eggs.
The Masuda Method is breeding two Pokémon whose language of origin is different, for example an English Ditto with a Japanese Pokémon. Eggs from that pair get extra shiny rolls. It started in Gen 4 and is named after Game Freak's Junichi Masuda, who described the bonus on his blog.
Bulbapedia's Masuda Method page counts 4 extra rolls in Gen 4, which works out to about 1 in 1,638. Serebii writes 1 in 2,048 for Gen 4. We use Bulbapedia's per-mechanic figure here.
Sword, Shield, Brilliant Diamond, Shining Pearl, Scarlet and Violet give one more reroll than older games, but a bug skips the first roll when breeding. The Masuda totals stay the same as before: about 1 in 683, or 1 in 512 with the Shiny Charm. The same bug means eggs bred with only the Shiny Charm (no Masuda Method) are about 1 in 2,048.