Pokémon Natures are a key feature of the games introduced in Generation III (Ruby / Sapphire / Emerald) and directly affect the stats of each monster. There are 25 in total, and we have a Pokémon Brilliant Diamond and Brilliant Pearl table to help you breed the best Pokémon possible.
Natures provide a ten percent increase in one stat and a ten percent decrease in another stat. Some natures are neutral, offering positive or negative zeros because they increase and decrease the same statistic. Enhanced stats [HP, Attack, Defense, Sp. Atk, Sp. Def, Speed] appear in red on the Pokémon summary screen. Decreased stats will have blue text. No nature affects HP.
One of the easiest ways to know which Nature to look for is to check your Pokémon's stats in the game or check their basic stats online. Gyarados, for example, has a high attack stat. You would like a Nature like Adaman or Jolly. Reduce his insignificant Sp.Atk stat to boost his attack or speed.
If you're still unsure which Nature works best, think about the types of moves and / or Pokémon you might encounter. Some Pokémon don't have obviously better natures, so experiment and see what you think works best for you and your teams.