>>14279380So basically, your poke has chance be just have a few random stats that it's natural stronger in, those are IVs
When you beat an opposing pokemon, your pokemon basically takes that opposing pokemon's highest state and adds a +1 to it's own next level up (exp: if you KO a zubat who's high stat is speed, the next time you level up you'll get +1 to speed)
They're really important for competitive pokemon because those little stat difference matter a lot, a game can complete decided on you being single point faster than your opponent or just defensive enough to live an attack on 1hp etc
It's time consuming and a pain in the ass to breed/train for these things (especially in the older games) which pokegen and battle simulators became more popular for competitive pokemon