For example, if a battery that drives a device generates 9 volts, it produces a difference of 9 volts at its two terminals. That is, if you measure the voltage at the battery’s positive terminal with respect to another node in your circuit or circuit, you will not see 9V. The positive pole of the battery is 9 volts higher than the negative pole. This potential difference drives a circuit.
If you are now using an external circuit with the Arduino, the ground voltage of that circuit is not necessarily (and usually never) the ground voltage of the Arduino. Likewise, Arduinos 5V will not be a 5V for this circuit. Therefore, you need a common reference point for both circuits to “ ground ” , from which the voltages of the battery and Arduino are measured. In a more detailed explanation, this would mean why you need a “full” circuit or loop.