I skipped a few generations and so I came back and had no idea what was going on. I watched a lot of youtube videos, lol. It is definitely complicated.
IVs- individual values. They're basically pokemon genetics. Each IV (attack, special attack, speed, defense, HP, special defense) can have a value up to 31. Each pokemon is assigned these and they'll help decide how good the pokemon is.
EVs- effort values. These are bonuses given to the stats (attack, special attack, speed, defense, HP, special defense) which are given based on what pokemon your pokemon defeats. You can also train these up via super training in gen VI.
Abilities- Each species has an ability which gives them a different advantage in battle. Some species have 2-3 abilities. Hidden abilities are abilities that a species can have but not in regular gameplay usually. You can get these from the friend safari or via horde pokemon. For example, I have a hidden ability heracross which has moxie. Every time my heracross KOs another pokemon, his attack stat gets a boost.
Honestly, most of it isn't important for just playing the game in itself. It's mostly in there for post game battling. It's kind of fun though- makes each pokemon a little more unique and means you can have different strategies with the same species. I super nerd and think about it like dog breeding, LOL. I want to breed and train the best stats possible. /nerd/