Ever spin a bike wheel in your hands?
 

Hold a bicycle wheel in your hands on each side of the axle and give it a good spin with a free finger. As long as you move the spinning wheel straight up and down (not side to side as if turning) there is no resistance to movement beyond just the weight of the wheel. But if you exert a turning or side force to the axle, you get a gyroscopic reaction. The strength of the reaction depends on how fast the wheel is spinning and how heavy the wheel and tire are, and the nature of the turning force. It is this reaction motorcycle people have called 'counter steering.'

Counter steering simply means using the gyroscopic force of the spinning wheel. You really owe it to yourself to take the front wheel off a bicycle and feel the reactions. It demonstrates the reality of the forces behind motorcycle steering. 'Counter steering' is a watered down and simplified phrase... its like the phrase 'zero gravity' used to describe the floaty movement in the space shuttle (actually, the gravity is only slightly less while orbiting the earth than while standing on the earth. The floaty movement exists because the crew are basically 'falling' through space in a constant environment. Its not about zero gravity at all.)

I'm not arguing about words. I'm saying gyroscopes behave a certain way and its a good idea to learn about them. For example, the front end of a motorcycle dips significantly when you steer sharply. Thats in the known nature of the gyroscopic effect. Counter steering doesnt mention this at all. Thats one example.

yeah, i used to do that all the time with my bmx tires. It was a trip before i knew the physics of what was going on there. I used to scrape up the inside of my arms. xD
Don't forget to mention centripetal force...