In cabling: A method if connecting audio equipment using 3 - instead of 2 - conductors. The third conductor, refered to as the shield, helps prevent electromagnetic interference, particularly in long cable runs and low voltage equipment such as microphones.
In equipment: The term "balanced" comes from the method of connecting each wire to identical impedances at source and load. This means that much of the electromagnetic interference will induce an equal noise voltage in each wire. Since the amplifier at the far end measures the difference in voltage between the two signal lines, noise that is identical on both wires is rejected. The noise received in the second, inverted line is applied against the first, upright signal, and cancels it out when the two signals are subtracted.