DT, the "Balanced System", in a nutshell, is this:
Rule 1. Level of beer carbonation is decided by temperature and pressure.
Rule 2. It takes a while for the beer to reach this equilibrium.
You can cheat, by cranking the pressure up and/or the temperature down. This will speed up the carbonation process, but if you leave it connected this way for too long you will over-carbonate.
Some people never bother balancing their system - they just crank up the pressure until the beer is fizzy enough, then they apply a different pressure to serve, or just give the keg an occasional 'burst' to keep it pressurised. Usually they disconnect the gas overnight. This works, but it means the beer usually gets either fizzier or flatter over time, because it is not balanced.
A properly balanced system is one where the temperature and pressure are appropriate to develop and maintain the right amount of fizz for you, and ALSO to serve at a comfortable speed. You can therefore connect a flat keg, and leave it connected for a year if you like. After a few days it reaches its equilibrium carbonation level, and providing the temp and pressure stay constant, so will the carbonation level and flow rate.
As mentioned above, it takes a bit of time to tune things just right, but once you have it set up you'll love it.