EVs, short for Effort Value(s), are what you get for beating certain Pokemon. This also makes stats go up, even though that Pokemon hasn't gained a level. The EVs are:
- HP (Health Point(s))
- Special Attack
- Special Defense
Based off of what Pokemon you faint whilst in battle you will earn the corresponding EVs from it. Slaking, for example, after you faint it in battle, it will give the maximum of 3 HP EVs to the Pokemon who fainted it.
EVs and IVs (Indiviual Value(s)) in the heat of the Competitive Play are too important to even forget about. Competitve Players send there time breeding, IV checking, and EV training to even be worried about anything else. This is where the full explanation of EVs begin.
EVs, first hand, are VERY much said in competitve play because it will calculate if your Pokemon can take a hit, be much faster, or hit much harder than others. This was now made easy thanks to Super Training, but even harder because you didn't know how much EVs you'ved trained for. So then hassles be done and gone there and here, but EVs are still very much said and done in competitive.
To sum it all up:
EVs, short for effort value(s), are what you gain towards defeating a Pokemon. They don't matter in-game, however they are widely used in competitive play. EVs are much random if you don't know who earns them and who even has which ones in the first place, however made simple with the Super Training.