In electronics, two points that have opposite electric potentials (one is positive, the other negative). This is not the same as being 180 degrees out of phase (although the results can be similar). Phase implies a relationship with time, polarity does not. What most engineers, consoles and preamps refer to as a “phase” switch is actually a switch reversing signal polarity.
Polarity is important when interfacing equipment, particularly speakers – you don’t want one cone moving in while the other moves out. Some designers feel that maintaining “absolute polarity” (no polarity reversal in a signal chain) throughout a signal path is important.
While tests don’t indicate that the ear can hear which polarity is correct, they do show that it may be possible to detect a difference between normal and inverted polarity signals. (Try it for yourself in a critical listening environment: Play a signal though a single speaker, then reverse the speaker wires and play the same signal again – remember to switch the wires back when you are finished!)