The purpose of the relay is to control the spindle, fans, exterior lighting, vacuum, etc...
The things that you don't want to keep turning on/off by hand, which may not need to be on all the time. (Eg, while moving fast to home, many of those listed things would not need to be running, wasting power and just making noise.)
The other purpose, besides control, is safety of that control. Those devices are high-power AC items which run at higher amps/watts than a simple microchip could control. As part of the safety aspect, using a relay allows a small voltage to control larger devices which have incompatible or dangerous currents. It is simply just an electromagnet light-switch, which isolates and protects you and your microchip-controller from those dangerous powers. (As opposed to a transistor-gate/switch, or other linked-circuit switch.)
All E-switches are not the same. Your looks like a dual-kill, but it could be a dual-position connection. (Dual kill will kill two legs of power in a 3-phase, or 2-phase system. For normal 120v home power, LIVE/HOT = BLACK and the NEUTRAL/COMMON = WHITE, respectively green is ground. Actually, black is not a standard as per regulation, but it is most often used in homes as LIVE. The white/grey wire is the same all over the house, thus common or neutral. Neutral is not GROUND.) A dual-position would have one set of contacts OPEN and one set CLOSED, they reverse when depressed and locked. You want to kill the LIVE wire, and you might want to POWER an "emergency warning light", or trigger an exterior breaker or break with the other contact.
You have to test the contacts to know which is which, if you don't have the instructions or can't find the documentation for that specific e-switch.
"There are no mistakes in DIY, only oversights that need adjustments."
"I don't care, I don't follow standards"