Short answer: Base Stats are basically experience points for your stats.
Long Answer: Stats are what you see on your Pokemon's detail screens and what attacks are calcuated based off of. Base Stats (or EVs) are a way of adding extra points in the six stats. Four base stats (EVs) in any given stat will grant an extra point of that stat at level 100. A Pokemon can only ever have 510 base stat points at a time, however.
This is wrong. Or inaccurate, rather.
Base stats are predetermined, unchanging values that are the same for all Pokemon of a species. They are notated as such: Atk/Def/SpA/SpD/Spe.
EVs are effort values, and are added on top of base stats as the Pokemon battles or super trains. They are capped at 510 EVs, with every forth EV adding to the base stat total.
IVs further add to base stats, and they are randomly generated numbers in each stat. Their value ranges from 0-31. They can be manipulated through breeding.