I see a lot mentioned about bi-wiring. I am not familar with this. I know you must have speakers that can be bi-wired and they are configured for bi-wire by removing a buss bar to seperate speakers and/or crossovers within the cabinet. I have also read that you need to have an amp that has bi-wire capability (two left and two right speakers outputs - and not to be confused with speakers A & B).

Can someone explain what takes place within each speaker when it is set up for bi-wiring? What are the advantages and disadvantages if any? What if my amp only has one set of left and right speakers outputs (but has something called loops for additional amps), Can you accomplish bi-wiring if you had two amps? If so how would it work?
The best thing is for you to try it yourself. To keep the cost down while you are experimenting, buy (or borrow) some plain ordinary 12 or 16 AWG bare speaker wire like the Monster cable stuff they sell at Radio Shack. Cut it in four pieces. Listen to some of your favorite music with the speakers wired both ways and decided whether it matters in your particular system or not. Every system is different. If any type of tweek does not work for someone, do not assume it does not work for the rest of humanity. It you find a difference and you like it, then go out and buy some better speaker cable.
Jostler, I respectfully disagree with your assertion that biwiring makes no sonic difference. I will attempt to explain why in my situation at least it does. I have a set of Martin Logan ESL's. If you remove the jumpers on the back of the speakers you can biwire. I believe when biwiring the amp gets connected directly to the woofer with one set of speaker cables and the other to the esl panel through the crossover. Given that the amplifiers damping factor is essentially the speakers impedance divided by the amplifiers output impedance you can see that in this case biwiring can influence damping factor as it would seem easier for the amp to sink the back EMF from the woofer without the crossover.
Liguy: I'm not familiar with your speakers, but what you're saying is unlikely. Typically, what goes to the woofer is whatever is connected to that set of terminals--either the jumpers or the second cable. Biwiring has no effect on where signals go once they enter the speaker. And the load facing the amplifier is also identical. After all, it's driving exactly the same thing(s) it was before.
Jostler, you are right and I stand corrected. Here is the real scientific explanation on why biamping effects sound. This came off the net if anybody is interested. When a current is pushed forward by the amplifier through the voice-coil in the magnetic field of a loudspeaker driver, the voice coil and attached cone move forward - the electric motor effect. However, the voice coil moving in the
magnetic field generates a back voltage - the electric generator effect. In a perfect driver, the back voltage matches the forward voltage, giving rise to the driver's dynamic impedance. In the real world, the back emf is distorted by nonlinearities in the magnetic field etc giving rise to harmonic distortions and so does not exactly cancel the forward voltage. These harmonic products from one driver's terminals end up across other drivers in the loudspeaker if they have common terminals and can cause further muddling of the sound. By connecting each driver through separate leads back to the amplifier, the distorted harmonics generated by each driver can be short-circuited by the low impedance output of the amplifier. The ability of the amplifier to sink this back emf from the low frequency driver is the damping factor. Where I went off course is not knowing that when the jumpers are removed the crossover is in effect halfed, so that the amp always sees the same impedance and does not effect damping factor. There now I feel better.
Liguy - You realize that when bi-wiring both the high and low side of the crossovers are still hooked together. It's just at the amp instead of the speaker. You can accomplish the same thing with larger speaker wire.

Damping factor is the ability of the amplifier to maintain a constant output voltage as speaker impedance changes. It can be very high in SS amps and good enough with tubes.

Take a woofer with a powerful motor and connect its terminals together. When you move the cone it feels like there is a shock absorber connected. Its a very strong effect. As you move the cone a current is generated that opposes the motion of the cone. In a system this effect improves the accuracy of the cone movement. So, it would be nice if there were nothing to impede this correction current generated by the speaker itself. Decent sized speaker wire and reasonable amplifier damping factor help. Typically, far more resistance is created by the crossover networks themselves. The slightest driver efficiency mismatch will have required the speaker designers to provide resistance to the louder driver. Resistance is unavoidably high throughout crossover regions.

Fully utilizing an amplifiers damping factor may be achieved with bi-amping or tri-amping, since there are no passive crossover components between the drivers and amplifiers. How much real world gain there is to bi-amping, I don't really know. I am undertaking a DIY speaker project shortly and it will be tri-amped with very high damping factor amps. When I am done with the project I still won't know ;-)