Balanced in layman's terms is using a separate amplifier circuit to drive each side of the headphone.
The benefits in electrical terms are:
-Doubles the effective slew rate (which is a fancy way of saying that there is twice as much wattage per channel)
-Dedicated grounds (meaning that each channel has a dedicated return path)
-Phase cancellation (meaning that the separate pathways provide a flip-phase signal that cancels distortion)
What this means for you:
-Doubled slew rate means more grunt. This means you'll get less clipping and have more headroom to drive and control the drivers properly
-Dedicated grounds remove the possibility of channel crosstalk, which means a cleaner, blacker background
-Phase cancellation means DRAMATICALLY lower distortion. Larger perceived soundstage. More distinct instrument and voice separation.
Any other questions let me know