Aggro

Aggro is a slang term meaning "to cause hostile NPC mobs to attack by getting too close to them." Short for "Aggravate". The Compass displays a white transparent circle, the Danger Zone (also called "aggro bubble" or "aggro circle"), that surrounds your character. Any enemy (indicated by red dots) that enters the Danger Zone (more than half of that enemy's circle has to cross into the Danger Zone) immediately becomes aware of your presence and is aggravated, causing it to attack you/cast spells on you as it's AI dictates.

Careful understanding and awareness of your Danger Zone is very important, especially if your teammates are low on health/energy or already attacking another group of enemies.

Breaking Aggro
An enemy breaks aggro if it no longer targets you and shifts to another target or moves away. There are several ways to break the aggro of computer controlled foes:
 * The most basic one is moving after acquiring aggro: A tank who is holding off enemy attacks will compromize his job if he decides to move, because enemies will assume he is fleeing and evaluate other targets. Most of the time, they will not go back to attacking him because tanks make the least desired targets for computer AI. The same applies to Shadow stepping.
 * Using AoE skills: Skills that rain down damage on foes (like Fire Storm, Maelstrom and Chaos Storm) will cause the computer controlled foes to flee after the first few hits of these storms. In addition, any skills with splash damage (damage to foe and foes adjacent/nearby/in the area) skills will cause the same effect if they are used in succession.
 * Moving outside a mob's area: Computer controlled groups do not follow forever, instead they will follow only to a preset diameter outside of the area they are supposed to be in. For stationary groups, this is roughly the radar area around them, for moving patrols, it is larger. One a player steps outside that ranger (even by one step) the foes will immediately turn back.
 * Running Away: If a player uses a skill that enchances movement speed to move away from foes, they will immediately try to find another target. They will not follow that player all the way to the edge of their range, even if there are no other targets to choose from.

Other Aggro Issues
There are additional issues that affect holding and breaking aggro:
 * Casting on an ally inside the enemy's aggro: If player A is inside the aggro of an enemy, and player B is outside that enemy's aggro, and then player B casts something on player A (a healing skill perhaps), then the enemy will become aware of player B (even though it has not seen him). Should player A do anything to cause the enemy to re-evaluate it's targets (such as moving), that enemy will be aware of player B and most likely go for him/her if they are a softer target in the enemy's AI.A common mistake is for monks to cast some enchantment on the tank after he has stepped into enemy aggro. Players are confused as the enemy seems perfectly aware of their presence even though they never stepped into that enemy's aggro circle.
 * Running past foes to get to other foes: A common practice by tanks is to rush past enemy tanks to get to enemy soft targets. Such a move however guarantees that the enemy tanks will also run past the tank. The computer AI for this is such that if it sees the player running past it, it will run past him/her for a few steps to see if there are others coming behind, then turn back and go for him if not. A common mistake is for casters to follow tanks too closely and get caught by surprise when they see the enemy running past the tank and going for them even though they thought they were outside the tank's aggro circle.