Natures

Natures are pretty straightforward, except for neutral natures, every nature raises a stat (other than HP) by 10% of its total while decreasing another stat (other than HP) by 10% of its total.

On the status screen, stats raised by Nature are hilighted Red/Pink, while decreased stats are highlighted Blue.

This is very useful as it can give a drastic increase to an invested and naturally high stat, while decreasing a stat you don't need anyway, such as Physical Attack on a Special attacker

Inheritance
When breeding, the Nature of a parent cxan be pass on to eggs by having that parent hold an Everstone, this guarantees the egg will have that parent's Nature.

This is one of the key aspects to breeding Competitive Pokemon.

Neutral Natures
These are effectively useless since they raise nothing while decreasing nothing.
 * Bashful
 * Docile
 * Hardy
 * Quirky
 * Serious

+Attack Natures
For Physical attackers that either have enough speed already and need more power, or don't need speed too much, the most useful is Adamant.
 * Adamant: -SpAtk
 * Lonely: -Def
 * Naughty: -SpDef
 * Brave: -Speed

+Defense Natures
For Pokemon that need more physical bulk either for balancing defenses or pumping up physical defense really high, all but Lax are useful depending on the set used.
 * Bold: -Atk
 * Impish: -SpAtk
 * Lax: -SpDef
 * Relaxed: -Speed

+Special Attack Natures
Same as +Attack natures but for the Special side, most useful is Modest.
 * Modest: -Atk
 * Mild: -Def
 * Rash: -SpDef
 * Quiet: -Speed

+Special Defense Natures
Like +Defense natures, again just for the special side, all are useful except Gentle.
 * Calm: -Atk
 * Careful: -SpAtk
 * Gentle: -Def
 * Sassy: -Speed

+Speed Natures
For already fast Pokemon that gotta go fast, or Pokemon that need a bit more speed to match up to common threats, Timid is best for Special Attackers, Jolly for physical, and Naive or Hasty for mixed attackers.
 * Timid: -Atk
 * Hasty: -Def
 * Jolly: -SpAtk
 * Naive: -SpDef