IV stands for ‘ Individual Value ’; it is basically a measure of the Pokémon’s inherent ability and can vary massively from Pokémon to Pokémon.
Think of it like this: some people are naturally better at some things than others. Likewise, every Pokémon you encounter in the game has its own individual statistical quirks, large unique to that individual creature, as a results of its IVs.
IVs in Detail
More precisely, each Pokémon has one IV for each of the six key stats (HP to Speed), with a value ranging from 0 (lowest) to 31 (highest).
At Level 100, the numerical value of the IV contributes to an equivalent boost in the corresponding stat (so an IV of 31 in Attack results in 31 extra Attack compared to an IV of 0), while at lower Levels, the boost is proportionally smaller.
Unlike EVs (covered below), IVs are fixed from the start and cannot be affected through training and, unlike Natures, they are not shown to you in an obvious manner.
For wild Pokémon, the IV spread is typically completely random, although with DexNav searching you can occasionally encounter Pokémon with 1 to 3 perfect (31) IVs, as indicated by the number of stars listed under "Potential".
Via breeding, you can pass down IVs from the parents and, with time and dedication, you can even breed Pokémon with up to 6 perfect IVs - the best Pokémon you can ever get.
Note : In the majority of cases, from X/Y and onwards, Legendary and Mythical Pokémon are guaranteed to have at least three perfect IVs.
So how do you work out IVs? Well, there are IV Calculators online and they are the only true way of reading a Pokémon’s IV values aside from training and hoping for the best.
Once you complete the game, you can speak with the IV Judge in the Battle Resort Pokémon Centre and he will give you textual information about your Pokémon’s IVs.
First he will tell you your Pokémon’s Potential , which basically gives you information about the sum of the six IVs. Obviously, the higher the sum, the better.
Next, he will tell you your Pokémon’s best stat(s) - the stat(s) that have the highest IV - and describe how "good" that stat is; he will even mention if any stats are beyond saving (IV of 0). Between these two, you can get a very good idea of your Pokémon’s IVs.
|Decent||0 to 90|
|Above average||91 to 120|
|Relatively superior||121 to 150|
|Outstanding||151 to 186|
|Best stat is...||IV|
|Rather decent||0 to 15|
|Good||16 to 25|
|Fantastic||26 to 30|
|Can't be beat!||31|