Hmm... I think there is something wrong in mattnin's post. Like I said in my previous posts, I am not engineer, but "the ESC has higher voltage" is incorrect.
Parallel capacitors will increase the capacitance in the typical case. Increasing the capacitance allows the amount of charge stored by the capacitor to increase.
The capacitor is used to filter ripple currents while the ESC is operating. So the capacitor removes voltage spikes, protects the ESC and allows you to be slightly faster before full throttle in comparison to not having a capacitor (full throttle speed is the same).
The best way to get good answers is to use the search function. There are plenty of good explanations here, but unfortunately, I believe this one is flawed. Maybe someone with better knowledge of electronics can confirm this.
I am not here to flame, but since some of mattnin's post seems to go against what I know (which may not be the truth), I want to post my 2 cents here too.