Effort Values, or EVs, are hidden training points that raise a Pokémon's stats, capped at 510 points in total and, since Generation VI, 252 points in any single stat. At level 100, every four EVs in a stat add one stat point.
Every species you defeat gives EVs to the Pokémon that gained experience from the battle. Pikachu gives two Speed EVs, Geodude gives one Defense EV, and so on. Wild battles during a normal playthrough scatter those points wherever the opponents happen to put them, which is fine for the story. EV training means choosing the opponents, or the training method, so the points land where you actually want them.
The caps shape the standard spreads. Since Generation VI a single stat stops at 252 EVs, down from 255 in earlier games, and the total stops at 510. Because four EVs make one point at level 100, the classic spread is 252, 252, and 6, maxing two stats and dropping the leftover into a third. Before Generation VI the same logic produced 252, 252, and 4, since points past a multiple of four were wasted.
Games have steadily made this less tedious. Vitamins add ten EVs to one stat, feathers and training items help in later games, and Generation VI added Super Training with a visible graph. Berries that reduce EVs let you fix a bad spread instead of starting over. In a close battle, a trained Speed stat is often the whole game.
In play"I put 252 EVs in Speed and Special Attack so my Greninja outruns most of the field."