Originally Posted by Some random guide
Effort Values (EV's) - Each of the six statistics for a pokemon has an effort
value. These values reflect the amount and type of battle experience that a
pokemon has acquired. When a pokemon defeats another in battle, the victor
receives effort value points to certain statistics; which stats receive points
is pre-determined by the defeated pokemon's species. EV's begin at 0 and are
capped at 255. Overall, a pokemon can have a maximum of 510 EV points across
all six statistics, and once this point is reached, the pokemon cannot gain any
further EV points.
Basically, they increase stats. You can either battle random Pokemon to gain EVs in random places, or you can fight certain Pokemon to increase a single stat's EV points (recommended because you can greatly improve a certain aspect of your Pokemon). Having the Macho Brace equipped doubles your EV point gain, and having Pokerus also doubles the EV gain (combined they are 4x).