Fairy magic.
My understanding is that counter steering is how you get the bike to change the lean angle one way or another. Once leant over, you steer into the corner the orthodox way, i.e. turn the bars left a bit to keep going round the left hand corner.
Once you are in the bend, leant over, the geometry of the bike pushes the front wheel around the bend, even though the very large gyroscope of the front wheel is trying its damnest to run upright.
If, in the bend, leant over, you took your hands off the bars, on a constant throttle, the bike would continue the same curve, going around in a big circle, until it ran out of petrol.
You can see what happens in GP races when riders are spat off in a corner. The throttle closes, drive reduces / stops, the bike stands up and carries on, on its own, straight ahead. Similarly, on an open throttle, the bike is leaned over, power pouring through the rear wheel, the front wheel is off the ground (it can't be steering, can it) and the bike is still cornering.
If, in say a left hand bend, leant over, you
pushed on the
right hand bar, the bike will straighten, reducing your lean angle.
If, in say a left hand bend, leant over, you
pulled on the
right hand bar, the bike will turn sharper into the bend, increasing your lean angle.
Chapter 9 of Keith Code's excellent book, describes it exactly.
Here is a pretty good picture, that shows it all. Look at the front wheel, look at where the Texas Tornado is looking and what his arms must be doing. He has dropped his right shoulder into the bend. This pushes the bar right hand out (away from the bend) you can see where the wheel is pointing. His arms are nicely bent (loose, not tense) and the grip on the bars must be relaxed.
And now the other way around. You can see, the left shoulder dropped into the corner, the left arm pushed forward, the wheel is pointing right (the black V of the SP's air intake in the nose of the fairing emphasises the centre line) and the bike cornering left.