EVs is the abbreviation for "effort values", which is a hidden attribute present in every Pokemon game and is kept mostly hidden. Every Pokemon's effort points get modified every time it defeats an opponent until the count reaches 508. These have an effect on your stats and are a good reason to wait until the end of the game to attempt building anything serious, since it will be easier to control what you're training on.
However, in Netbattle, EVs are distributed through simple slider bars, giving you full control.
Using EVs to Your Advantage
HP (Hit Point) EVs
This should ideally be set as a multiple of 16 to draw full potential from the Leftovers item. Setting it so your max HP as 404 also lets you make Substitutes that resist Seismic Toss (and the occasional Night Shade) without breaking, mostly usefull to Sub-Punch Blissey. HP should also be favored over both defense stats on most Pokemon, especialy those with a low base HP stat, since it will make them more resistant overall (Dusclops is a good example of this). For Pokemon with a lot of HP like Snorlax and Blissey, defense should be raised instead for more resistance.
This is pretty straight foward, raise it if you want your Pokemon to hit harder with physical type moves. Also, if you use a Pokemon with only special moves, lowering this stat's IV as much as possible is good to avoid confusion damage.
Considering the metagame revolves around physical moves a lot more than special, this is the stat you'll want to pump on your walls. Blissey, Skarmory, Swampert, Suicune and the likes all benifit from this greatly.
Mostly important on sweepers. There are some speed tiers that act as milestones. For example, 394 is the highest speed number outside of ubers, Dragon Dance users should aim to beat this after 1 or 2 DDs, Salac users should also beat this after their berry activates. 300 is also a good number as it lets you outspeed a good number of things. Low speed Pokemon like tanks and walls could leave this alone altogether without worrying much.
Special Attack EVs
Your strength with special type moves, pretty simple. Raise this to hit harder with them. It would be best to use a nature that lowers attack but benefits in another stat.
Special Defense EVs
For some reason this is never used a lot. The main Pokemon to use EVs in this is Snorlax if you want him to be a special wall.