A support style is a helping style that causes no damage on its own, but can easily turn the tide of batle in your favor. The styles cause status effects that slow, stop, or disorient their targets. Support styles often won't win a battle on their own because they normally do no damage. However, with Chi strikes, support styles can cause some pain.
Among the more useful support styles are Storm Dragon, Paralyzing Palm, and Spirit Thief. The first two styles can stun your enemy for a time. Storm Dragon must be bought, but if you follow the Open Palm, you can get Paralyzing Palm for free from the Black Leopard School in the Imperial City. Spirit Thief steals chi and is unique among all styles for this reason.
These examples easily show how support styles can turn a surefire loss into a come from behind win. Steal some chi to heal, or stun your foes to land a critical strike. They may not do damage, but support styles may be some of the most useful in the game.
Note: Demons are immune to support styles.