Rather than just being a superficial personality, Natures actually affect the growth of a Pokemon. Each nature increases one of its stats by 10% and decreases one by 10% (by the time it reaches level 100). Five natures increase and decrease the same stat and therefore have no effect.
In most cases it is preferable to have a nature that decreases either Attack or Special Attack for Pokemon whose strengths are the opposite type of attack. Espeon, for example, favours Special moves, so it's best to use a nature that decreases its Attack since it won't be used.