This is Joonil Park, and here's a video referring to the term steering versus counter-steering. Now, counter-steering is a term used a lot in motorcycling and motorcycling education. The term counter-steering comes from the act of leaning, or initiating lean and go of a motorcycle.
A motorcycle traveling above eight, nine miles per hour uses lean angle to change directions and not steering. Steering is something you do in a car. On a motorcycle you initiate lean by pressing in the direction of the turn. You do not want to just press forward with a left-hand grip to turn left, you want to press in with your whole body and lean your body English into the turn, all the while keeping your throttle steady, as steady forward motion is when a motorcycle is most stable.
Do not confuse counter-steering with counter-weighting, however. Counter-weighting is opposing use of your body weight, and body English, to help stabilize a motorcycle's weight when going slow, for U-turns and figure eights, for example, that is steering. Counter-steering is what you do in a higher speed corner. You can almost think of counter-steering like turning a motorcycle's lower half by rotating the front wheel to the right, making the top half lean to the left, and lean angle again is what dictates the direction change of a motorcycle. Keep that in mind.