Press the normally-closed pushbutton and see what happens to voltage across it with & without the capacitor in the circuit.
What's going on:
How does a hammer work? Force = Mass x Change in Speed. A rapid change in speed makes a large amount of force on the nail head.
Same thing here; opening the switch makes a rapid change in current that produces a huge voltage spike (voltage = inductace x change in current). This causes arcing damage to switch contacts, along with electromagnetic noise in nearby electronics (static on the radio). Since the switch is already a capacitor, the solution is to just put another capacitor in parallel with it to absorb the change in voltage, much like a water hammer arrestor in a plumbing system.
