EVs (Effort Values) are basically experience for your six stats. 4 EVs will level up a stat.
Maximum of 255 EV per stat, or 63 of that stat.
Maximum of 510 EVs per pokemon, or 2 maxed stats.
Each pokemon gives a certain amount of EVs when KO'd (Usually 2-3), and X/Y has Super Training to make this even faster.
IVs (Individual Values) are basically genes. They cannot be changed whatsoever, and you have to breed new pokemon in order to see any change.
IVs range from 0 to 31. A level 100 pokemon with 31 Attack IVs will have a bonus 31 Attack. If you halve the level, you halve the bonus stats.
All pokemon will have randomized IVs, 0-31. This means you might randomly happen upon a Caterpie with perfect 31 Speed IVs.
You breed a new pokemon named Babby. One of Babby's IV's will be copied from its father. Another IV will be copied from its mother. A third IV will be copied from a random parent. The remaining three IVs will be randomized 0-31.
You can manipulate these mechanics to get a pokemon with 3 or 4 perfect IVs. You can get all 6 perfect, but that takes literally forever.