The ability to charge and discharge quickly makes them handy in a couple of ways. Using a capacitor in parallel with a heavy reactive load like a motor or power amplifier can provide an extra "shot" of power when a load is suddenly applied. That's handy if you want to put big subwoofers in your car, but isn't used too often in a yard haunt.
What does come in handy is the capacitor's ability to filter out spikes in voltage. Halloween props very often involve the use of devices like pneumatic solenoids, relays, and motors that present a highly reactive load to a power supply. It's also very common for those props to be triggered or controlled by sensitive controllers. Putting capacitors in parallel with the power leads of the controller smooths out any voltage spikes the props might create. The charging and discharging of the capacitor smooths out the peaks and dips in voltage.
Think of it this way. Lets say your highly successful haunt has a straight queue line. As people come up in groups of 2 or 3 (or 10) the pressure on the line (voltage) rises and falls.
Now if you take a chapter from Disney's attraction design and add a "stretching room" like the Haunted Mansion, the flow of people is smoothed out.
Capacitance is measured in farads, and capacitors have a maximum voltage rating. For filtering purposes the smaller the farad rating, the faster it charges and discharges. That means that smaller capacitors filter higher frequency spikes, while the larger ones handle lower frequencies.
