The big difference between motorcycles and bikes is in the presence of or lack of gyroscopic stability. A motorcycle at speed has ALOT of heavy 'turning stuff' that wants to say put in it's current plane of rotation. The faster you go on a motorcycle, the more it wants to stay put. That's why any knob can do "top speed" runs on their buddies sportbike...because it doesn't take anything at all to do it, just a twist of the throttle. A motorcycle at speed can ride fast in a straight line with or without the bonehead at the helm (If that seems like a harsh way of putting it, I am probably talking about you)

It's this gyroscopic stability that requires intentional counter-steering in order to get a motorcycle to turn. On a bicycle, especially a road bike, there's very little rotational momentum (tires/wheels are all light weight, and of course no engine spinning at 8k rpms) so initiating a turn on a bike requires so much less counter-steering that it's done naturally by most people. You can safely control a bike without ever being taught the principle. So don't feel like you're missing something important if you don't wholly understand all this. If you can negotiate corners, you're already putting it into practice. The only time it helps, as stated above, is in panic situations where having a little more understanding of "how to make the bike turn sharper in the middle of a turn while panicking." In this case, it could help you, but in the same way could easily crash you immediately too, depending on how controlled your reaction is.

-Jeremy