An unbalanced cable has two conductors (wires)--one for the signal, the other for ground.
A balanced cable uses two conductors plus the ground for a total of three. The extra conductor in the balanced cable carries an inverted version of the audio signal.
Its use is this: when the signal arrives at the amplifier, the inverted one is flipped over and recombined with the other signal. The cute trick is that any noise added by the cable is flipped too. Cable noise is positive in both wires; the final flip makes one noise signal negative and it cancels out the noise signal in the other wire.
Balanced configuration has real advantages for very long cable runs which can pick up a lot of noise, and it is pretty much indispensable for live recording. For shorter runs, it may or may not make a difference depending on your gear and your situation.
Also, balancing adds considerably to component cost, since the circuitry to produce the second, inverted signal at one end must be just as high-quality as the circuitry for the non-inverted signal, and so must the flipping and combining circuitry at the other end. Balanced wires are more costly than unbalanced, too, for equivalent quality.
So IMHO if you need it you need it, but better if you don't need it.
Lastly, it is unfortunate but some components which are advertised as balanced do not actually use truly balanced circuit configuration, although they do have the double signal (Cannon or XLR) connectors. Buyer beware!
