I'll give this a shot here.
Lets picture a Di/Bi-pole speaker mounted on the side of a room. For simplicity, we will say that the speaker has two full range drivers. While the speakers are usually at an angle, again from simplicity, we will say one driver faces forward, and the other driver faces rearward.
Can you picture that?
Now, a positive going electrical pulse enters the speaker, and moves both drivers forward away from the magnet structure. These speakers are electrically in-phase, since a positive voltage results in forward movement of the speaker.
But, let's look at that movement in relation to the room. Since one driver faces forward, and the other faces rearward, they are moving in the opposite direction. Relative to the drivers, the cones are both moving forward. But relative to the room, one cone moves toward the front of the room and the other moves toward the back of the room. They, relative to the room, are moving in the opposite direction.
They are electrically in-phase, but mechanically out-of-phase. This is a Di-pole.
If we reverse wire the back speaker, so the amp(+) connection goes to the (-) of the rear speaker. We now have drivers that are mechanically in-phase, but electrically out of phase.
When a positive voltage is applied, the front speaker moves forward away from the magnet, but the rear speaker moves backwards toward the magnet.
Now, again stepping back and considering the whole room, we see that the speaker are actually both moving in the same direction. A positive voltage moves both driver cones toward the front of the room.
Again, they mechanically move in the same direction, but since they face in the opposite directions, they have to be wired opposite.
EDITED: The corrected Phrase should be - Electrically, Be In Doubt. Mechanically IN-Phase, and electrically OUT of Phase would be DI-POLE.
ERROR: Mechanically in-phase, but electrically out-of-phase. These are Bi-pole speakers.
Now, it is hard to explain, but again, simply picture the movement of each cone relative to the room.
In the Di-pole configuration, the front speaker move forward toward the front of the room, and the rear facing speaker moves toward the rear of the room.
In the Bi-pole, the front driver moves toward the front of the room, and so does the rear facing speaker. They both move in the same physical direction.
Which is right? Well, both and neither. Each wiring method has its own advantages and disadvantages. It is up to you to determine which configuration you like best, and that is also why many speakers like this come with a switch, so you can have either configuration. Try both, and keep the one that sounds best.
A simple diagram would go a long way to explaining what I mean, but I'm not that good in graphics programs, so it would take some time to draw out.
steve/bluewizard