Individual Values, or IVs can be compared to the Pokémon's "Genes".
They range from 0 to 31 for every stat and are added to the pokémon's stat for their value at level 100. (example: a level 100 Tyranitar with no Effort Values and 0 IVs has 310 HP, while if it had 31 IVs, it would have 341 HP)
These stats are provided randomly for every pokémon you catch or breed, and although it may seem that 31 points do not make much of a difference, they are indeed important for Ace Trainers to put into account when breeding pokémon with perfect natures/stats.
An example of how IVs can be important: user: Johnny B Guud has a Terrakion with 0 Attack IVs. At level 100, he will have an attack of 358 (with an attack improving nature), while a Terrakion with perfect Attack IVs would have 392 Attack. This small difference can be the tie between a OHKO and a survival with 1 hp (it happens more than you think)
Fortunately for us, Ace Trainers and Pokémon Breeders specially, these "IVs" can be bred so the quest for the perfect pokémon can begin.
The process of breeding IVs is as follows, for a Male Nidoran and a Female Nidoran:
1. The kid's IV's are generated randomly, for example: 7/27/31/14/19/2, in HP/ATK/DEF/SPA/SPD/SPE format 2. Three stats are inherited from his parents, and these can stack. The game makes three checks to the pokémon's stats:
a) First check: a random stat is chosen from either the Mother or the Father and passed upon the kid (HP/ATK/DEF/SPA/SPD/SPE)
b) Second check: a random stat but HP is chosen from either the Mother or the Father and passed upon the kid (ATK/DEF/SPA/SPD/SPE)
c) Third check: a random stat but HP and Defense is chosen from either the Mother or the Father and passed upon the kid (ATK/SPA/SPD/SPE)
This means that HP and Defense are harder to pass upon the son, but do not give up hope! There are ways to make sure the IVs are passed on; Power Items!
By letting any of the parents hold a Power Item, you can make sure that that stat will be passed upon the offspring. Say you put a Power Weight (Increases the HP gain of the holder on battle) on the Mother, who has a perfect IV of 31 on HP
If the first check (a) selects the Mother, you are sure to have a kid with perfect IVs on HP. The other checks will be random, but if you're either lucky or patient you'll eventually get the stats you are looking for. Remember: only three stats are inherited per Pokémon and these can stack: you can get the Defense IV from both the Mother and then the Father, clearly wasting IVs...