Why does my switch need to be wired in this fashion?
For the grounding it's easy. Basically a switch can have not 2 but 3 state. Basically


High when pressed 
Undefined when unpressed and not grounded
Low when unpressed and ground








simulate this circuit &ndash; Schematic created using CircuitLab

Grounding it will allow you to make sure the output low, without that it's a short circuit. So basically you'll use a pull-up or pull-down resistor for that.

They are connected in parallel means they are not connected one after each other but side to side. Example







simulate this circuit

So from what I read in your question, the switch sound like a "master switch" who can act on both of the 3 other switch. If pressed, it's like all the switch are pressed. But hard to tell without precise schematics.