Countersteering simply starts the bike falling in the direction you want it to go. E.g. steering slightly right leans the bike to the left for a left hand turn. When you recenter the bars, the left turn is completed. Countersteering makes it possible to turn more sharply and at higher speed than just using your weight to lean the bike in the direction you want it to go. If you try to turn the bike with the handlebars by direct steering, you will go the wrong way. Sheldon Brown makes it clear that this is the way essentially all two wheel (wheels in tandem) vehicles are turned. Sheldon Brown's Bicycle Glossary Cn - Cz