Welcome back into the world of crazy critters! I myself lost interest in Pokemon after Gen 2 and coming back into it playing Soulsilver was mind-blowing.
Pokemon natures affect how your pokemon grows in its stats, usually by boosting one stat and hindering another. I use this chart:
http://www.psypokes.com/lab/natures.php
Abilities is a little more difficult to explain but it basically adds additional effects in battle. For example, Levitate means ground-type moves will miss on a Pokemon that can Levitate, even if it isn't a Flying type. I'd recommend Bulbapedia for that.