I think you need to go back to the basic idea of an electrical circuit. Current must flow all the way round a complete circuit. That's why it's called a circuit.
Without getting into electrons or holes as the carriers, any current that flows out of the positive power supply/battery terminal will go through whatever the load is, an LED, a motor, lots of LEDs etc and (this is the critical part) then it has to flow back to the negative terminal. In an Arduino and a lot of other electronics the GND terminal is the thing that is connected to the power supply/battery negative.
Steve