Aggression is an act of a non-neutral character attacking a character of another alignment. This cannot be done at Astrub, zaaps, banks or dungeons, but on most other maps. The target has no way of refusing, unlike a challenge. The loser of an aggression suffers the normal penalties for being defeated in combat.
You receive Honour Points for defeating people you aggress, and lose points for people you fail to kill. The amount of points gained/lost is proportional to the level of the players on either side, so for the maximum of 100 points, you must defeat someone at approximately the same level as you.
A monster that triggers combat with players that move too close is usually called aggro or aggressive instead.
Typical usage: I want to aggress that guy. He aggressed me. That monster is aggro. The monster aggroed me.