EVs are what determines your Pokemon's stats when it hits Lv 100. They're there so that pokemon aren't alike, so that pokemon of the same species can differ.
Basically, all pokemon in the wild give off Effort Values, or EVs when you defeat them. Depending on what their dominant stat is, you will get certain and sometimes multiple EVs from that pokemon.
EG I catch a Pidgey and train it against one Rattata. The rattata gives 1 EV in speed, so that is added to my EVs.
Problem is, you can only get a maximum of 510 EVs in total, and a maximum of 255 in a stat. To max out a stat, you train a pokemon so that it gets 255 EVs in that stat. For example if I wanted to max out my pidgey's speed, I'd train against 255 Rattatas.
-- Every 4 EVs you get will amount to one extra point in that stat when you reach level 100. It DOES NOT necessarily mean that your pokemon will recieve an immediate noticeable stat change, however you will notice the difference to a non-EV trained pokemon when you reach Lv 100. --
Once you have recieved all 510 EVs, your pokemon will no longer recieve EVs and its stats will go up according to the EVs it obtained in its early training.
Easier ways to fill up your EVs - Vitamins... Vitamins (eg Carbos, Calcium etc) give 10 EVs to the stat they work on HOWEVER they cannot be used once that stat has gone over 100 EVs. Nor can they be used more than 10 times. You can also only give a pokemon a total of 51 vitamins (eg 10 for all normal stats and 1 in HP)
Macho Brace and Pokerus increase the amount of EVs you recieve from from wild pokemon by 2, and both can be used together. Say, if the Pidgey I caught had Pokerus, and I gave it a Macho Brace to hold, then if it defeated a Rattata I would get 4 speed EVs instead of the usual 1.
