Effort values (abbreviated EVs and previously called Stat XP) are attributes which give bonuses to a Pokémon's stats and improve differently depending which Pokémon they defeat. These bonuses, in the form of effort points, are gained in addition to bonuses gained by increasing level. A Pokémon which increases in level using a Rare Candy instead of battling does not gain any EVs, making it weaker than a Pokémon who increases in level normally.
Roughly speaking, defeating fast Pokémon increases Speed better than fighting slow Pokémon, defeating Pokémon with high hit points improves HP more than defeating Pokémon with low HP, and so on. For example, fighting 100 Machop will improve a Pokémon's attack stat more than fighting 100 Abra of the same level, whereas the Abra will improve the Special Attack stat more. (copied from bulbapedia)
tl;dr EVs are things you get from defeating pokemon (which vary from pokemon to pokemon) that affect how your stat value grows. If you defeat 100 Abras, you will get 25 Sp.Atk EVs, because your stat goes up 1 point for ever 4 EVs (100/4 = 25 EVs). A Macho Brace doubles the amount of EVs you get per pokemon (100/2 = 50 EVs). And there are power items which quadruple the amount of EVs you get (100/1 = 100 EVs).
I hope that explains it.
