Alright.

The easiest way to think about how caster works is to imagine a wheel and how it moves during steering, or, you can illustrate with a roll of tape on your desk.

Using the tape example, use a rubber band or something sufficient to hold a pencil through the centerline of the roll of tape, orienting the roll like the tire and wheel would be. Now, during steering we all know that the wheel will turn left or right about it's steering axis, and this can be demonstrated by holding the pencil perpendicular to the table and twisting. Now, if we tilt the pencil back towards us and turn the wheel, what happens?

Can't really tell can you? Do the same thing, and this time, hold the pencil with your other hand and hold the tape slightly above the table surface. What you should notice is that when you turn outboard, the wheel "digs in" to the table, and when you turn inboard to the pencil, it seems to lift slightly. Any time the contact patch of the tire changes it's "distance" up or down, it tries to carry or lose more weight. When the tape tries to "dig in" it's effectively trying to carry more weight, which is what you want for cornering, more inside weight for stability, especially since the natural tendency is for items of mass to travel to the outside radius.

Now, if you do the same observations but this time tilting the pencil away from you, you'll notice that when the tape turns outboard, it tries to lift from the table.

This isn't an entirely bad thing. The idea is for the inside to be forced to carry more weight by raising it's height, which will then catch the weight of the outside wheel as the front tries to re-establish an equilibrium. This normally means the outside tire takes a lot of abuse on corner entry, and that corner entry is a bit more squimish.

This isn't entirely the front tire's fault though. What I haven't mentioned is the weight transfer effect to the rear wheels.

Now, in an ideal chassis, the frame is absolutely rigid, and as we all know, if you lift on one corner, the weight has to be carried by another corner. This is where cross-weight comes into play in the grand scheme of cornering weight transfer.

I hope I didn't go through that too quick, any other questions?