IVs, or Individual Values, are those things that influence stats. An IV of 31 is considered a perfect (flawless) IV and an IV of 0 is considered bad. The rater always gives you the highest IVs for a Pokémon and you know they're perfect if they "can't be beat"; the same rater then mentions any 0 IVs, or says nothing else if there are none.
More on IVs.
Not a breeding thing, but related, here are Effort Values.
EDIT: I see now I was beaten to answering, but the links may prove helpful.