Natures affect the stats that they modify. Natures cannot affect HP, simply because there are no natures that change it. Natures either do nothing, such as Serious or Bashful, or they multiply one stat by 1.1 and another by 0.9 (always round down). This is useful for boosting stats that need a little more and downgrading stats you don't use at all (usually one of your attack stats).
You cannot change a Pokemon's nature. If you want a Pokemon with a certain nature, you have to breed for it and hope you get the 1/25 chance for the nature you want, but you can always breed with that Pokemon again if it doesn't give you the nature you want.
Here's a scenario: a Victini has an attack stat of 299, but a serious nature. If another Victini has a nature that boosts its attack stat, and the same conditions as the other one, then its attack stat could hit 328 maximum.
A list of natures can be found here. It might be able to explain it better than I can. The most common natures you'll see are usually Adamant, Modest, Timid, and Jolly, so if you want to enter competitive, it is helpful to memorize what those four do first.
Good luck! :)