I'll start by describing electrical phase, which will give you an idea of acoustic phase. With electrical phase, picture an AC sine wave, phase describes a particular point in the time of the cycle. There are 360 degrees of phase in an AC cycle, 180 for positive alternation, and 180 for negative alternation.
Where this applies in audio mainly relates to crossovers used for drivers, and to a certain extent the drivers themselves. Crossover networks are a necessary evil, and use inductors and capacitors to act as a filter to prevent damage to the drivers used, the drawback is that crossover networks introduce a phase shift. An inductor opposes change in current flow, when current flows across a conductor, a magnetic field is generated, and when a change in current flow happens, the magnetic field generated opposes the change in current flow for a period of time. Think of it like a car going 60mph, it just won't stop instantly and back up. With an inductor, current will lag voltage to a degree, a purely inductive circuit will show current lagging voltage by 90 degrees, which is what we consider a 90 degree phase shift. A capacitor operates by having two conducting surfaces (plates) that are slightly separated from one another. They are not electrically connected. Capacitors can store electrons, but cannot allow them to flow from one plate to the other. In an AC circuit, a capacitor will store electrons for part of the first alternation, and then release its electrons and store others when the current reverses direction. Because of this, a capacitor, even though it interrupts a circuit, can store enough electrons to keep current moving in the circuit. Opposite to inductors, a capacitor will cause current to lead voltage to a degree, a purely capacitive circuit will show current leading voltage by 90 degrees. Some crossover filters allow you to combine the two and the original phase will be recreated precisely. This is what is referred to as "phase-coherent", the high and low pass outputs are considered complimentary to each other. 6db/octave slopes offer the best performance when referring to amplitude and phase response, but most drivers aren't able to use them because of it's gentle slope.
Hopefully I haven't lost you by now. Anyway, the effect that this has on a speaker system is that the speakers are attempting to replicate the electrical signal that is coming to them, and when you use multiple drivers, you have to assure that they are in proper phase (firing at the same time) in order to provide a synchronous sound. Phase shift is especially noticeable on imaging and frequency response, they will fall apart if the drivers are far out of phase.
Phase control is a bit more complicated, when designing a phase control circuit for a specific application it requires a pointer diagram to display the differences in the voltage/current relation of the system's drivers output, which is affected not only by the crossovers, but the actual driver positioning as well. With an electrical phase control circuit, you are basically choosing a corner frequency and introducing enough phase shift to compensate and align the drivers together, essentially bringing them in phase with one another at a certain frequency.
If I may add, in simpler terms, what phase is and how it affect us.
There are four basic slopes for crossovers. 6 dB, 12 dB, 18dB, and 24 dB slope / octave.
If you use the same slope on the tweeter as you do on the midrange, and bass; then you will be in phase.
If you chose to go with a 12 dB slope on the tweeter and 6 dB slope on the mid, and woofer; then you will be out of phase.
Why?
Because the mid and woofer will already move outwards while the signal has not reached the tweeter yet.
When the tweeter finally starts to move outwards, the mid and woofer will already start to move inwards, thus creating out of phase.
(Push verses pull)
In this case the difference is 180 degrees out of phase.
Now:
On self powered subwoofers: you will find a 0 degree and 180 degree phase switch.
This switch allows you to switch in and out of phase, so that your sub is in phase along with the rest of the speakers because of the location that the subwoofer may be at.
Because it is believed that bass frequencies are omni-directional, you may put the subwoofer wherever it is convenient for you.
Just switch back and forth between 0 degrees and 180 degrees to determine which is best for your setup. There is no right or wrong way. It all depends where your sub is located in conjunction with the other speakers in the room.
Johnathan, if I were to give you the specifics on the system that a friend and I are designing/building, would you be able to instruct me on how to get proper imaging and phase?