warning first post, and its late, I hope I don't get myself banished for such a long post if it doesn't make sense
I saw some good explinations on counter-steering here, and I haven't been riding all that long, but I would try explaining its because the tires on a motorcycle are so rounded, forgive me if this doesn't make sense, this is my first post and I'm not always the best at explaining things, but I thought I would give it a shot.
When you lean, even keeping the wheel straight the bike turns because you are not on the bottom of the wheel anymore when you lean, you're off center, which because the side of the wheel follows a different path than the bottom... ie: its a curved surface the bike naturally starts to do a circle, or a turn.
The bottom of the tire in the center constantly hits in a straight line as the wheel turns when its straight, the sides of the wheels obviously curve around the edges of the tire.. curving, not following a straight line like the center of a tire does. If you roll a tire upright, the center of the tire touches, and the next surface area that touches as it rolls comes right after the first in a straight path on the tire's surface.
If you were to tilt the tire and roll, the following spot that is going to touch is not directly ahead of current section on the tire in a straight line because the wheel curves, the wheel is turning on the ground as it follows that line on the tire because its on the rounded part of the tire.
The reason you have to countersteer is because when you lean in a turn you end up on the side of the tire, because of how much the tires curve on the bike, the amount of lean needed to make the bike start turning is very minimal. As you'll notice on easy or gradual turns, you barely have to lean the bike at all to get it to turn.
With sharper turns and higher speeds you have to lean the bike more in order to compensate for the g-forces pushing you towards the outside of the turn so that you do not stand up straight and come out of the turn early. If you were to keep the wheel straight as you leaned into a sharp or higherspeed turn, the amount of lean required for you to keep the bike from standing up and coming out of the turn because of the g-forces would put you far over on the curved section of the tire. That natural route the tire would want to take because of how far over you were on the tire would be alot sharper than the turn you were on. Remember it doesn't take much lean with the wheel straight for the bike to start turning.
Countersteering causes the surface area of the tire that is touching the ground to be more towards the center of the wheel which is more flat, (thus a less curved part of the tire - remember it doesn't take much curve on the tire to get the bike to turn) while allowing you to lean low enough in the turn to compesate for the g-forces pushing towards the outside of the turn.
So basically to sum it up, because you have to lean in a turn to compensate for the force pushing out of the turn, it would put you on a section of the tire that would cause you to turn sharper than you want, counter steering turns the wheel so that the tire is touching more towards the center and giving you the correct curviture to get through the turn. The amount you have to lean to compensate for the g-forces of a turn would put you would put further on the curve of the tire than you would want if you kept the wheel straight.
Does that make sense to anyone or should I have just kept this post in my head? I would hope that someone who already understands it can read this and get what I meant, but not sure it'll help you understand if you didn't already get it. I didn't understand it when I first started, but you have to do it, especially at higher speeds and sharper corners and it works. [Add on] Also, on a side note, the curviture of the tire conveniently helps the bike to lean over naturally to one side or the other as you counter steer, making it easier to manuever the weight of the bike. You don't have to try and "man handle it" or throw you weight around to get it to do this.
lol, wow, if this post sucks, I am sorry because I re-wrote it twice trying to make it more understandable lol. Maybe that is the reason someone earlier in the post said they were just gonna skip explaining the physics of it.... lol Hope it helped.
thanks for reading this whole darn thing, please comment and let me know how I did.
(edited to insert paragraphs