Short for aggressive or aggression. Can be used to describe how a person is behaving. Also in MMORPGs such as World of Warcraft it refers to an enemy attacking you if you get too close to it. In MMORPGs certain enemies have different ranges that will trigger them to attack. Some enemies can attack even when you are fairly far away and some only attack when your characters is right next to the enemy or in very close proximity. Higher level enemies tend to have a larger range than lower level ones.
"Chill out, what is with the aggro today?"
"That idiot in our group just pulled aggro on a group of elite murlocs!"
"You're pulling fucking aggro from them! Run for it!"