what is a relay and why would it be hooked up to a capacitor?

"The capacitor across a relay coil is likely to be there to keep the voltage steady during high speed operation; otherwise the switch might "bounce," act jumpy for a moment before keeping good contact."

Huh?

The bounce of relay contacts is a mechanical property and the only way around it is a mechanical solution.

Wet relays were designed for this reason since the mercury would keep the circuit path during bounce/chatter.

De-bouncing a switch INPUT to a logic circuit can be done with an RC path, but that also adds propagation time.

A relay is two components built together. One of the parts is an electromagnet (a coil), the other is a switch. When the coil is energized it pulls on the switch which makes it have (or loose) contact.

The reason behind it is that the coil can be operated by one battery source, with the switch operating a different circuit.

The capacitor across a relay coil is likely to be there to keep the voltage steady during high speed operation; otherwise the switch might "bounce," act jumpy for a moment before keeping good contact.

You should know that there are alternatives; a capacitor maybe there for timing, intentionally releasing the electromagnet in so many seconds. Also these days there are solid-state relays.

A relay is an electromechanical device that has contacts that open or close depending on the coil voltage or current. I can't say much about the capacitor, because I have no idea about the specific circuit; however, it would be a bad idea to put relay contacts acroos a cap without some resistor to limit the current.