The power capacitor is on the ESC to protect it. The fet's on the ESC work as switches. When they want to shut, the current passing through them coming out of the battery can't stop at once, it will have to be routed somewhere else, because otherwise the fet will have to burn it off as heat; not good! The Capacitor will take up that current. Even, without the capacitor, the fet''s might even be hampered to shut. On 4 cell, you might not need the capacitor, because there's less current flowing, but it might help efficiency (read run-time).
You don't want to use just any capacitor. The regular capacitor's are not designed to work at the high switching speeds of today's esc's. If you destroy one (by soldering it wrong way around for instance) get a new one from the ESC's manufacturer.
I have been using a regular capacitor on my esc, and started to feel more like an on-off-switch with it. Also it ran quite hot. Don't make my mistake!

The capacitor might slighly increase punch, because it might help the battery for a short time (think in milliseconds) under really heavy loads, like hard acceleration from a standstill.