The courtesy wave is the silent "thank you" on the road. If someone in oncoming traffic waits to let you take a left turn, you give them a courtesy wave as you go by. Or if someone lets you cut in front of them, you wave to them behind you. It's an accepted way of thanking another driver.
The wave can be used no matter if you're a driver, biker, or pedestrian. When I'm biking I do the wave also as a "thank you for not killing me" gesture. If I notice a car doesn't squeeze me out while passing, but actually waits until they can change lanes: courtesy wave. If a car in oncoming traffic is trying to go left and waits until I've passed to make the turn: courtesy wave.
Basically if a car acknowledges my presence on the road, I want to give them a small sign of appreciation.
