IV breeding is one of the most important components of pokemon and their stats. IV's are the pokemons DNA. They can not be changed and when a wild pokemon is caught or one is hatched, ivs are randomly generated. But, you do have some control over your ivs. When the parents of your bred egg have great ivs, there is a good chance the baby will too. Also when your pokemon is hatched, it will say something at the bottom like "MIschievous". That can hint the ivs of a stat. Here is a list below.

HIT POINTS
31-Often dozes off
30-Loves to Eat
29-Likes to Relax
28-Likes to scatter things
27-Often Naps
26-Often dozes off

ATTACK
31-Likes to thrash about
30-Proud of its' Power
29-Hot Tempered
28-Quick tempered
27-A little Quick-Tempered
26-Likes to Thrash about

DEFENSE
31-Capable of taking hits
30-Sturdy Body
29-Good perseverance
28-Good endurance
27-Highly persistent
26-Capable of taking hits

SPEED
31-Alert to sounds
30-Likes to run
29-Quick to flee
28-Somewhat of a clown
27-Impetuous and silly
26-Alert to sounds

SPECIAL ATTACK
31-Mischeivous
30-Highly Curious
29-Very Finicky
28-Often lost in thought
27-Thoroughly cunning
26-Mischeivous

SPECIAL DEFENSE
31-Somewhat Vain
30-Strong Willed
29-Somewhat Stubborn
28-Hates to lose
27-Strongly Defiant
26-Somewhat Vain