Balanced wiring was first used by telephone companies at the beginning of the twentieth century in order to reduce hum on phone lines. When they're not balanced, cables naturally act as antennas, drawing interference from any number of nearby devices such as lights and wall outlets.
Balanced wiring removes hum and other interference by winding together two closely spaced conductors. A positive signal flows in one direction and a negative flows in the other. This process balances all signals leaving the cable and unbalances all signals coming in. Through shielding, balanced cables also reject any noise and interference from outside sources.
Balanced cables come in a few different forms. They are most common in live music and music recording applications. XLR microphone cables and quarter-inch tip-ring-sleeve musical instrument cables are perhaps the most widely seen examples of balanced cable wiring. But telephone lines and a variety of other data lines can also be balanced.