Aggressive fighting style is opposed to defensive fighting: higher damage is dealt (133 % max) and two-handed weapon speed is increased by up to one second. However, defenses are reduced.
This type of fighting works well when you fight with a group of people and are not the one taking the hits and needing to defend yourself. You hit more often but parry less. Axes are considered good weapons for aggressive fighting, since they do not parry anyway.
It can be toggled via the "fight window". If the fight window is not displayed it can be toggle through the menu by pressing the "o" key.