Technically speaking, balanced connections have to do with equal-impedance wires such that any interference affects both equally. If you have impedance mis-matching, the advantage of balanced signalling becomes less.
Differential signalling is the +/- signals that people often refer to.
http://en.wikipedia.org/wiki/Balanced_audio#Differential_signalling
Depending on how the amplifier is designed, a balanced audio system may or may not sound better. Often times, people compare balanced amp A with unbalanced amp B and automatically assume any differences between the amps is because one is balanced and the other isn't, which most likely isn't the whole story.