What's the use of the Super Capacitor keys?

Those are both "OUTPUT" signals.

Using the screenshot as an example, if you set a laser (that has a INPUT signal to trigger the laser) with the UP ARROW, as long as this battery is full, the laser will keep firing.

In the screenshot you have a decoupler. Let's say you set the decoupling command as DOWN ARROW. As soon as this battery is depleted, the decoupler will trigger.