I'm no wiring wizz but at a guess it simply cuts the power to the starter, so the 2 big wires are the posative feed to/from the starter, then when you press the button it connects them...simple huh...
However the small wires are probably an ignition feed, it de-activate the switch, it will only become active when the ignition is switched on, for which youll still need a key.
Thats how most "simple" push button starters work, so insert key, press button and it starts. Without key = no go.