IVs is short for Individual Values, EVs for Effort Values, Nature is the pokemon's nature (you see it in their summary: Timid; Adamant; Jolly; Docile; etc).
Individual Values is basically the stat ranking of a pokemon once you catch it. It cannot be changed unless you catch another. It ranges from 1-31, 31 being the best. Each stat has its own IV; ATK, DEF, SPD, SP ATK, SP DEF...)
Effort Values are the hidden stat bonuses you achieve while defeating enemies. A single pokemon can get 510 EVs total, 255 max for each stat. Every 4 effort value is one more stat point into that one specific stat. Defeating certain pokemon gives EVs of a certain type and different quantities of it. This is one of the most important factors when participating in competitive battles, so be wise when distributing these hidden values! It might seem tedious, but there are a lot of things that speeds up the process, the simplest one is knowing where to train. Try this:
http://www.gamefaqs.com/portable/ds/file/925602/48969
Nature also affects one's stats. Normally, it weakens one stat to boost another. Although there are natures that has no affect whatsoever. Although these balanced natures sound decent at first, it isn't very good, since some people can perform better when boosting one stat for another. For the sake of argument, say Mewtwo (whose a Sp.ATK beast), usually goes with Timid or Modest nature. Both of these nature reduces ATK which isn't one of Mewtwo's strong assets.
Here's a list:
-Lonely: +Attack, -Defense
-Brave: +Attack, -Speed
-Adamant: +Attack, -Special Attack
-Naughty: +Attack, -Special Defense
-Bold: +Defense, -Attack
-Relaxed: +Defense, -Speed
-Impish: +Defense, -Special Attack
-Lax: +Defense, -Special Defense
-Timid: +Speed, -Attack
-Hasty: +Speed, -Defense
-Jolly: +Speed, -Special Attack
-Naive: +Speed, -Special Defense
-Modest: +Special Attack, -Attack
-Mild: +Special Attack, -Defense
-Quiet: +Special Attack, -Speed
-Rash: +Special Attack, -Special Defense
-Calm: +Special Defense, -Attack
-Gentle: +Special Defense, -Defense
-Sassy: +Special Defense, -Speed
-Careful: +Special Defense, -Special Attack
Copied that from gamefaqs.
Hope it helps.