In every battle, you gain EV points. For example, defeating a Bidoof gives your Pokémon 1HP EV. Same is true for Starly and Speed. Beating Spiritomb gives you 1 point from both Sp.Def and Def.
EV training is when you're training your Pokémon on only* Bidoof for HP or Machop for Attack. So, it is better to keep training on lower level Pokémon because you get less EXP and same EVs, so when level-up, your Pokémon gains MORE new stats.
*not only, but mostly