The switch is basically just a break in the connection to allow the starter to engage. With the clutch pedal depressed, (clutch disengaged) the circuit is complete and the starter will be able to be engaged with the key turned on and the button pushed. When the clutch pedal is released (clutch engaged). the circuit is open and the starter is not allowed to function. The bypass switch is simply a jumper harness that bypasses the clutch switch and "fools" the system to think the clutch pedal is depressed. The only issue with this that you have now removed a safety feature from the vehicle as the engine can start without pushing in the clutch - therefore it can start in any gear (including reverse) and could cause injury, damage, or even death, so be careful if you do this. It should only be used as either a tester to see if the switch is bad, or in an emergency so you can get home in cases when the clutch switch actually does fail
I was 100% going to say all of that but he beat me to the punch... 
