Each individual Pokémon has a Nature that influences its stats. This Nature is randomly determined upon encountering the Pokémon and cannot be changed legitimately once caught. Each Nature raises one stat by 10% and decreases another stat by 10%. No Natures influence HP, and certain Natures don't affect stats at all.
Prior to catching them, a Pokémon's Nature can be changed by having the Synchronize ability on the first Pokémon in your party, setting the Nature to be the same as the Pokémon with the ability.
After catching it, the nature can only be changed by /pokeedit or similar commands, but can also be effectively changed by using a Mint on it, which changes the stats boosted and reduced to reflect another Nature instead.
Within NBT tags, Natures are stored as numerical IDs. These numbers are only useful when editing Pokémon NBT data externally.
|Nature||Increased stat||Decreased stat||ID|
|Careful||Special Defense||Special Attack||24|
|Rash||Special Attack||Special Defense||20|