Sure, carbonation in beer is controlled by 2 things, pressure and temperature. These two factors determine how much dissolved co2 is held in the nectar.
So lets say you've got a keg in the fridge that's had time to equilibrate at 45 degrees under 10 pounds of pressure, you're co2 level will be at just over 2 volumes of co2. Now at 1 atmosphere, the nectar will only hold 1.3 volumes and that's way below styel guidelines not to mention that when the pressure is released from the nectar, (like when you put it in a glass), you will get foam and a quick drop in co2 volume to the 1.3 and less as the temp rises.
What the counter pressure bottle filler does is pressureize the bottle with co2 pressure before the nectar is allowed to flow into it. This maintains pretty close to the same pressure in the bottle as is in the keg. This allows you to fill without foam or oxidation.
I know you're asking, why would you want to bottle from the keg? Well let's say you force carbonated a batch and decide that this is the best stuff you ever made. Oh no, you didn't bottle any to send to competition or to give to friends, or to send to high ranking heads of state. You just whip out the handy dandy counter pressure bottle filler and fill away, capping each bottle very soon after filling.
I hope this has helped.
Yes, I know it's a bit much but I just got off work and am into my 3rd homebrew

I know, I know, you can't shut me up when I've been drinking.
