RAK said:A balanced audio connection has two wires, one of inverted polarity to the other. (For instance, in an XLR connector, pin 2 carries the signal with normal polarity, and pin 3 carries an upside-down version of the same signal.) However, an XLR plug also carries a third connection - pin 1 is used as an earth to shield the other two. The received signal is the difference between the two signal lines. This signal recombination can be implemented with a differential amplifier where the negated signal is tied to the negative terminal of the operational amplifier. A balun may also be used instead of an active differential amplifier device. Much of the noise induced in the cable is induced equally in both signal lines, so this noise can be easily rejected - the noise received in the second, negated line is applied against the first, upright signal, and cancelled out when the two signals are added together.
The separate shield of a balanced audio connection also yields a noise rejection advantage over a typical two-conductor arrangement such as used on domestic hi-fi where the shield is actually one of the two signal wires and is not really a shield at all, but relies on its low, but in practice not zero, impedance to signal ground. Any noise currents induced into a balanced audio shield will not therefore be directly modulated onto the signal, whereas in a two-conductor system they will be. This also prevents ground loops.
All that makes sense to may, and always has. Whatever it means to you, that's wonderful too.
Note that balancing does not require an out of polarity signal to work, and that it is the gear, not the wire, that has the polarity inversion.