To Simple Questions with this, I think. Mind you, a lot of people get confused about EVs, because they are generally hidden.
Basically, EVs are bonuses to the stats that a pokemon has, which you can add yourself through battles (rather than base stats which are fixed for that pokemon, and natures and IVs which are randomly chosen). You can gain a total of 510 EV points, and every 4 points adds 1 point to a stat, up to a total of 255 in one stat (although 252 is agreed as the best maximum, since the extra 3 points are lost when rounded down.) So, the standard (but not always the best) use of EV points is to add 252 to two stats, leaving you 6 points for a third stat, for a total of +63 points and +1 point respectively. The extra points often make the difference between survival and failure, which is why EV training is important.
Gaining EVs is not a hard process, although tracking them involves a bit of paperwork. Basically, gaining EVs invovles battling certain opponents, because each opponent defeated adds either 1, 2 or 3 points (depending on evolution) to a stat. A way to speed up the process is to use vitamins, since each vitamin used adds 10 points to a stat, up to a maximum of 100, although this is an expensive way, it does save a lot of time.
When you think about it, EV training is quite simple, but there is quite a bit to remember, so things aren't always immediately obvious.
