In very basic terms, its the amount of runway required to permit two takeoff scenarios.
1: Accelerate Stop = Accelerate with all engines to a point called Vef, (1 second prior to V1) at this point the engine fails,you initiate an aborted takeoff and stop at a certain point.
2: Acclerate Go = Accelerate with all engines to a point called V1, where the engine fails, continue the takeoff and achieve a screen height of 35 feet at a certain point.
When the distance required for 1 is the same as 2, then its a balanced field. In a lot of cases it will be all of the runway length available, but not always.
Please remember you asked for the simple version!
Mutt.