EVs are effort values.
EVs are used for Pokemon to gain higher stats than usual, mainly for competitive play.
Every Pokemon that is caught brand new (meaning it didn't KO anything at all, will be ready for EV training) will be able to EV train.
EVs are hidden values in the game that determine a certain stat that your Pokemon gain as they level up.
Every time you KO a Pokemon, that Pokemon that KO'ed it (or even received experience from Exp. Share) will gain a certain number of EVs (varying from Pokemon, and other things).
For example, if you KO a Tentacool, you will gain 1 EV in Sp. Defense. Every 4 EVs = 1 stat. So if you KO 4 Tentacruels, you will gain 1 stat in Sp. Defense as you level up somewhere.
There IS a maximum number of EVs every Pokemon can receive though:
252 is the max EVs for each STAT.
and 510 EVs is the max for the total number of EVs in total.
I'm sorry if my explanation wasn't that clear, because l tried to simplify it as much as possible, please read the link below for complete information and l hope you get great Pokemon!