IVs, or Idiocy Values, are the main factors in determining the overall usefulness of a Pokeymon. The more IVs you have, the more dumb you are, so the more likely you'll do whatever sick, grueling training exercise your twelvie masters tell you to do. That's what we here at Stealthrockpedia think, anyway.
Some say that these 'IVs' are like genetics (somehow), and they influence how strong a Pocket Monster is at its birth, making this factor independent from any training the Pokemon may go through in the last pathetic years of its life. Since we have yet to see a Pokemon actually being born, this theory cannot be supported.