Perhaps someone will chime in if I get this slightly wrong, but...
A brushless motor is driven by changing the current in the motor wires in exact synchronization with the speed of the motor. You want the current through the windings to be in one direction as it pulls towards a magnet pole, and then you want to reverse direction to push away from that pole and attract towards the opposite pole as it revolves around. The three wires for the motor power allow this to occur in a special wave pattern where the inbound current on one or two wires exactly matches the outbound current on the other wires. It's somwhat similar to the way 3-phase power wiring works.
The 5 wires to the magnetoresistive sensor are to tell the controller exactly what position the motor is in, so the current in the power wiring can be applied appropriately to power the motor. The red and black probably power the circuit, with the other 3 wires providing a position signal.
I'm not positive on the other 3 wires you mention, but the brown and black is probably intended to go to a kill switch (usually connected to a brake lever so there will be no power applied when braking). In a bike controller the 'extra' wire would go to a pedalling sensor, but that doesn't seem to apply for a scooter.
Didn't the controller come with a wiring diagram?
-Mike