Answer:
Modest is one of 25 natures that Pokémon can have; each Pokémon has a nature, and each only has one. Which nature it has affects its stats slightly. Modest increases its Special Attack and decreases its Attack.
It also affects which type of berry a Pokémon likes; if you give your modest Pokémon a Dry berry, it will become happier, and if you give it a Spicy berry, it will like you less.
For more information, see http://bulbapedia.bulbagarden.net/wiki/Natures