Simply, a balanced cable cancels out interference from other electrical equipment and radio frequencies. A unbalanced cable suffers from interference and as a general rule is only used for low signal gear and short distances.
It is straight forward to identify if a cable is either balanced or unbalanced, it is possible by looking at the connector on the end of the cable. An unbalanced cable has two points and a balanced cable has three. Below of images if typical connectors you may find.
The inside of a balanced cable will have two lines, the signal cable will run straight down the middle with the grounding cable surrounding it. The grounding cable not only helps shield the cable form interference from other electrical equipment but also carries part of the audio signal too. This does a good job of reducing the interference that gives you the annoying hum, but the cable itself acts as a antenna.
The longer the cable the worse. This is mainly the reason they are only used for short runs, like guitar and keyboards (which produce low level signals anyway) and should not really be any longer then 6 meters.
A balanced cable has three wires, two signal and one grounding. These are used to cancel out the interference, simple and ingenious! How? Well, the two signal wires carry the same signal but with the polarity reversed. This leaves you with silence, not much use!
The secret is when the signal reaches its end point (amp etc) it will revert the signal back to its original orientation. Because each signal wire picks up the same noise along the way, once reverted back you are left with the original signal intact, without any noise. Simple!!