Section 1: Introduction to IV's and Nature

Ok, so nature was covered in guide to being a top trainer but it doesn't hurt to get a bit more detail while breeding does it?

Ok so here we go!

Introduction to IVs and Nature

Individual Values, or IVs for short (sometimes also called Diversification Values or DVs) are essentially numbers that act as the Pokémon's "genes". Every Pokémon has a "gene" for each of its stats (HP, Attack, Defense, Special Attack, Special Defense and Speed), which is a number between 0 and 31. The higher the number, the better that particular stat will be for that Pokémon. The player cannot alter the IVs of any Pokémon in any way. They are set in stone the moment you encounter that Pokémon in the wild, or the moment that Pokémon’s egg is given to you.

Since the player cannot change the IVs of his or her Pokémon, the temptation would be not to even bother about IVs. However, IVs are very important, since a good IV may add up to 31 to a particular stat when the Pokémon is at Level 100, and sometimes even more than that, if that stat is being boosted by a favourable nature (see the next paragraph). It also turns out that, while breeding, some IVs of the parents are actually passed to the baby, and so, if the parents already have a few good, or even perfect IVs (31), then the baby would have a chance of inheriting them. Thus, breeding for perfect IVs is not only important, but also possible without cheating, and that is the whole scope of this guide.

In addition, each Pokémon has a nature (sometimes also called personality). Most of these natures modify that Pokémon's stats in some way. There are 25 possible natures. Here is a list of them and what each does to your Pokémon.
Nature Stat increased by 10% Stat decreased by 10%
Lonely Attack Defense
Adamant Attack Special Attack
Naughty Attack Special Defense
Brave Attack Speed
Bold Defense Attack
Impish Defense Special Attack
Lax Defense Special Defense
Relaxed Defense Speed
Modest Special Attack Attack
Mild Special Attack Defense
Rash Special Attack Special Defense
Quiet Special Attack Speed
Calm Special Defense Attack
Gentle Special Defense Defense
Careful Special Defense Special Attack
Sassy Special Defense Speed
Timid Speed Attack
Hasty Speed Defense
Jolly Speed Special Attack
Naive Speed Special Defense
Hardy None None
Bashful None None
Docile None None
Quirky None None
Serious None None

If you want your Pokémon to have the highest speed possible, for example, you'll want it to have a 31 Speed IV and a nature that boosts Speed. This guide will also show you how to breed such a Pokémon.
Abbreviations Explained

If you find a group of letters, or one letter, it means that what follows works only for the games referred by those letters. The letters stand for the following:
Abbreviation Game
R Pokémon Ruby
S Pokémon Sapphire
FR Pokémon Fire Red
LG Pokémon Leaf Green
E Pokémon Emerald
D Pokémon Diamond
P Pokémon Pearl