Aggro is a jargon word, probably originally derived from the English words "aggravation" or "aggression", and used since at least the 1960s in British slang. In games such as Heroes vs. Monsters, aggro denotes the aggressive interests of a monster/NPC towards your hero.
For example, you may read of a player who died while fighting one mob because she aggroed another mob — that is, another mob decided to attack her because she got too close to it, or for other reasons. If a mob is under attack by more than one player, then the mob will aggro onto (i.e., will begin to attack) the attacker with the highest threat.
Aggro is understood to be the condition of a particular mob attacking a particular Hero, while threat is the numeric value that each attacker has towards each character on its threat list. Managing aggro is one of the most important aspects of the game because it determines how much damage the group receives and where the damage ends up.
Holding aggro is done by (usually) one person (the tank) who uses his abilities to make the enemy attack him and no one else.
Aggro control is the art and work which is done by the player to force the mob to attack the tank(s).
Mobs tend to have initial aggro once they enter the play field. However having a hero near the right side of the screen, will increase the chance that they will focus that hero. Basic attacks will draw aggro away from your heroes who have low defense.
Aggro-control in a party
Tanks can use taunt to aggro mobs in an AOE area, if someone else aggroed it, but in the best groups a tank will only rarely need to taunt — though many still will just in case. A tank can hold aggro without ever having to taunt if every class is aware of how aggro works.
During the fight
Who a mob attacks
If healers/DPS draws aggro
Taunt or charge with your tank to draw aggro away from the cleric/dps. The mob (or powerful individual will tan attack your fighter, and your cleric/dps (read as squishies) will be safe.