Aggro means that something is attacking you. For example, in a dungeon, the tank wants all of the "aggro" or everything attacking him. If you have aggro, it means that something decides to come after you instead.
An aggro reducing ability is a spell of some kind that will help you "drop aggro" which basically means the spell has a good chance to make the enemy stop attacking you.
DPS stands for Damage Per Second. It is usually only tracked in raids/dungeons. You want this number to be as high as possible so you combined with the other DPS players can take down mobs/bosses more efficiently.
Heroics are just harder versions of regular dungeons. The payoff is better though as you obtain betetr gear, more gold and things like that from the Heroic.
Cata = Cataclysm
WotLK = Wrath of the Lich King.
BC = Burning Crusade
Vanilla WoW = The original World of Warcraft
I could help you out with dungeons as well. Just ask me anything you are unsure of and I can tell you maybe what I would do in certain situations.
Oh and don't worry about looking bad, it is part of the learning experience lol.