[font=trebuchet ms]This post covered some of what you're looking for.

Now, about coil tapping:

If you connect a wire to one of the windings in a coil, that new connection is called a tap. If this tap is connected to one end of the coil, the windings between the tap and that end terminal are shorted out, effectively reducing the number of turns in the coil. If this was done to a single-coil pickup, the result would likely be a much thinner sound.

In a tapped humbucker, the tap connection is made between the two coils. Then, if the tap is connected to one of the other coil terminals, that entire coil is shorted out, leaving only one coil working. So a humbucker can be turned into a single-coil pickup at the flick of a switch.

A variation on this technique is to make both ends of both coils available. This is what is meant by a four-wire pickup. With all of the wires out where you can decide how to connect them, you can set up a simple coil-tap system, or you can use a switch to select either series or parallel connection of the coils.

A series connection means that the current flows through one coil, and then the other one (like a series of events). In a parallel circuit, part of the current flows through each coil at the same time (parallel paths).

I use this system on my guitars because the series connection gives the full humbucker sound and the parallel connection gives a (almost) single-coil sound. I prefer using a parallel-connected humbucker instead of coil-tapping because both coils are still in the circuit, so I still get the noise cancelling effect that humbuckers were invented for. DiMarzio has some wiring diagrams you can study to see how all this goes together.
[/font]