What part of this did you not understand?
Now, why does this make a difference in corner negotiation. We must understand that the wheels of a motorcycle act as a gyroscope, and that this gyroscopic effect is increases in proportion to speed. One property of a gyroscope that applies here is the reaction called precession. When a gyroscope is acted upon by an outside force (in this case, gravity, when the bike is leaned over) it will react, or precess by causing an opposing force acting at 90 degrees to the applied force. Since gravity acts downward through the center of mass of the bike, the opposing force from the gyroscopic effect of the wheels will act at 90 degrees to this, which in a flat corner will be parallel to the ground, opposite to the lean of the motorcycle.
This reaction has its pros and cons. The gyroscopic effect is what keeps the bike from falling over in a turn ( in spite of gravity). It is not momentum that causes this! However, this effect also means that as you try to lean your bike in a fast sweeper, or try to accelerate through a curve, there is a force acting to straighten the bike up, which may cause you to drift wide, and then perhaps cause the worst!
When you shift your weight into a corner, you effectively move the center of mass of the entire rider / bike package further from the tire (contact patch). The effect is that resultant force pulling the bike down into the turn is greater. (This is the same principle as using the length a lever to increase resultant force)