Balanced power systems are most commonly seen in 120-Volt power circuits used in the US. Normal wiring has one neutral wire that is always at (almost) ground potential and another wire that carries the 120-Volt AC. There is also a separate safety ground wire.
In balanced power there are two 60-Volt lines (rather than one carrying 120 Volts) that are each out of polarity with the other, and a neutral wire. The Voltage difference between these out of polarity lines is 120 Volts, so connected equipment will get a full 120 Volts between its power input pins. Due to the differential nature of a balanced power scheme some types of interference that can manifest on electrical lines become cancelled in much the same way that balanced audio lines allow for interference they pick up to be cancelled. Balanced power is typically created from a normal AC electrical supply by using a transformer with center-tapped 120-Volt output and the grounded center tap, which provides the two 60-Volt legs.