Polarity refers to whether two pressure waves are in compression or rarefaction. Phase refers to where specifically in their compression or rarefaction stages they are.
Say you are listening to drums in mono on two speakers that are connected with correct polarity and are far away from any boundaries. The drivers of both speakers should move out and in together. When they move out, the air is in compression. When they move in, the air is in rarefaction.
If you were to place a microphone at your listening position and record how the air pressure varies with time from each one separately, you'd end up with two waves. The "top" (positive) part of each wave would be the compression. The "bottom" (negative) part of the wave would be the rarefaction. We refer to them as positive or negative with respect to the resting state (no movement of the speaker drivers) which is no compression or rarefaction. Since the drivers move together, so do these waves; both waves occur at the exact same time. At your listening position, when both speakers are on, they add up to a bigger wave that has the exact same shape but a larger pressure than each constituent wave. You hear a solid beat that is tight, articulate, room-filling and emotionally satisfying.
Let's suppose however that one driver was slightly "slower" than the other. In that case, one would start before the other. So you'd have two waves again like before but they would not be "rising and falling" together. In other words, they would not be synchronized; the two waves would not be in phase. They're still the same shape as before but not coincident in time. At your listening position, they add up to a bigger wave sometimes but not at other times. You hear a distorted beat that is soft, fuzzy, flat and emotionally confusing.
Phase displacement can be translated into a time displacement with some simple math. If the two waves are out of phase enough, their polarity may change. This happens when one wave starts going positive while the other starts going negative. Another way to say this is when one speaker starts to move in while the other is starting to move out. This is the condition where they are out of phase by 180 degrees and the polarity of one is inverted with respect to the other.
Note that, for many reasons, two speakers will never be in perfect phase alignment. With digital filtering and active speakers though, you can get pretty darned close.
So bottom line here is get the wiring correct and Brendo's suggestion of a 9V battery for woofer testing is a good one.
P.S. a good analogy to understand polarity vs phase is two pin-wheels with each half painted a different color. If the colors are perfectly "aligned" on both as they spin, they are in phase and of matched polarity. If one starts to slow down relative to the other, the phase between them changes. Eventually they may reach a point where the top and bottom of them are two different colors and this is where they've switched polarities.
