Aggressive is one of the three "postures" available to pets; the others are Defensive and Passive.
An aggressive pet will attack any mob that enters its aggro radius. In this mode, the pet will be constantly starting fights with mobs in its vicinity. This may be useful to a hunter who wants to grind a lot of monsters, but it can be very detrimental in an instance, where drawing the attention of a swarm of monsters can quickly wipe out a party.