If you've been traveling over 20 mph, you've been counter-steering... Simply put, it uses leverage to cause your bike to shift it's weight in order to change direction. Push left-go left, push right, go right. It's really important to know how to effectively counter-steer in order to avoid objects, or to go fast around a race track.
I'll let someone else provide a link or explain the physics. But in mechanical terms, above 15-20 mph, when you push a direction on the handlebar, you cause the front wheel to deviate from the direction of travel. Because of the inertia of the bike, it will want to continue to go the previous direction. But since the front wheel is now out of alignment, the bike will try to trip over in the direction you pushed - effectively shifting it's weight. Since this is most of the battle in getting a bike to turn, it's a very effective tool. I think the first Kieth Code book talks about it well also.