Natures can be viewed at the Summary Page of a Pokémon. They are important to the game because they determine what berries a Pokémon will like and dislike. The natures are randomly generated when Eggs are hatched, with a 1/21 chance of each one. Since five natures are under the any category while there are only four in the others, a Pokémon that likes any berry is most likely to hatch.
Pokémon with the natures Hardy, Docile, Serious, Bashful, or Quirky can be fed any berry and remain happy with it. However, these Pokémon receive less EXP than those with a favourite flavour.