A balanced signal can be a little tricky to explain. You’ll find balanced audio in professional audio gear, from microphones (such as the venerable SM-57) all the way to mixers and professional PA amplifier inputs. Your guitar amp input, by the way, is not a balanced input. Nearly all consumer equipment that has an analog audio output uses unbalanced audio as that has less expensive circuitry.
The way a balanced signal works is that a source device outputs a signal as two identical audio waveforms, but of opposite polarities on the two wires (leads). The plus (+) lead is called the non-inverting lead and the negative (-) lead is the inverting lead. Thus, the signal is balanced between two waveforms that are perfectly out of phase with each other.
In the receiving device, the polarity of the inverting lead is reversed, so now the signals are in phase.
Balanced audio has a few benefits. Balanced source devices usually have a very low output impedance, as compared to unbalanced source devices. This allows the signal to be driven much longer distances on cable with less signal loss.
Also, because of the phase reversal, balanced signals reject noise that may be induced onto the cable. If noise is induced onto the cable, the noise will be nearly identical on both leads, and since it was externally induced, the noise will be in phase on both leads. However, at the receiving device, remember, the polarity of the inverting lead is reversed. So, the wanted signals are now in phase and are additive. But, the unwanted noise that was externally induced on the cable is now out of phase and is cancelled out, much like a humbucking pickup. However, modern balanced gear usually use devices called, “differential amplifiers” to accomplish the phase reversal. This cancellation is referred to as Common Mode Rejection (CMR).
Interestingly, the Les Paul Recording model had balanced outputs. Les Paul had wanted a guitar that provided a balanced output as it is a cleaner, more noise-free signal.
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