Safety circuit on ignition system.
If the bike is in gear, it won't start unless the clutch is disengaged. With that wire broken [circuit open] the bike will no longer start in gear even if you disengage the clutch.
I'm guessing you've only tried starting it while in neutral, which is why you haven't noticed anything different.
Since Yamaha uses an either/or setup- you'll be fine. Suzukis on the other hand require both to start.