Atk = Attack stat, dictates power of physical attacks, usually. (Karate chop, tackle, spark, zen headbutt)
Def = Dictates resistance to physical attacks
Sp. Atk = Special Attack power (Thunderbolt, water pulse, flamethrower, watergun)
Sp. Def = Resistance to Special attacks

EV = Effort Value - There's one for each stat, and you get one added to the relevant field when you defeat something. Whatever field the thing you defeated was best in (e.g. Zubats give speed EVs) you get a point for that field. About 4 points grants +1 to that stat (So killing 4 zubats gives my pokemon an extra point when it levels up next) (I think)
This is why trained pokemon are stronger than rare candied and wild pokemon.
The catch is that you can't get any more than 255 EVs across all your pokemon's stats.

IVs are different. I think each IV is directly equal to 1 extra stat point. Thing is, the max is 32, and IVs are dictated at the pokemon's creation; no two pokemon are the same, usually. You can't change, view or control IVs directly. (You can breed IVs, but that's specialist stuff)
This means that you could raise two of the same pokemon exactly the same way, and still have one that's stronger than the other.