EV stands for
Effort
Value and it determines the stats a Pokemon will have when leveling up. Fighting any Pokemon in the wild or from a trainer will give your Pokemon EVs. When you EV train your Pokemon, you're basically finding the Pokemon that gives the EVs that you want so that you know what EVs go where.
Examples:
- Infernape: 252 EVs in ATK / 252 EVs in Speed / 6 EVs in HP
- Gyarados: 88 EVs in HP / 248 EVs in Atk / 4 EVs in Def / 168 EVs in Speed
Here's an example of how useful it is:
A Jolly Infernape without EVs in Speed will have a
283 speed stat, while another Jolly Infernape with 252 EVs in speed will have a
346 speed stat. The Jolly Infernape with the 252 EVs invested in Speed will attack first in battle.
Assuming both Speed stats are 31 IVs.
When you battle random Pokemon in the wild (etc), you have no clue what EVs your Pokemon gets.
PS. There's an alternative to EV training in X/Y. It's Super Training (the mini-games on the Player Search System).