The wire connector that connects the neutral wires together is removed to check for loose wiring.
In the diagram above, the A phase circuit breaker is turned off on a multi-wire branch circuit. The wire connector is removed from the neutral wires for inspection in an A phase receptacle electrical box. In the A phase receptacle box:
The neutral wire that comes from the electrical panel carries 0 V.
The neutral wire that goes to the A phase receptacle carries no voltage.
The neutral wire that goes to the B phase electrical box is 120 V.
In the diagram above, the A and B phase circuit breakers are turned on on a multi-wire branch circuit. If the neutral wire is removed from the A phase receptacle, there will be 0 V on this neutral wire. There is an unbroken current path from the B phase receptacle to the neutral bar in the main electrical panel.