Greater voltage creates more magnetism pulling the solenoid's core in further against the spring loading, moving the pointer.
For DC, this magnet flips one way or the other, indicating by the exposed color (red or black) which lead is connected to positive.
Solenoid voltmeters are extremely rugged and not very susceptible to damage through either rough handling or electrical overload, compared with more delicate but more precise instruments of the moving-coil D'arsonval type For "go/no go" testing, there is no need to read the scale as application of AC power creates a perceivable vibration and sound within the meter.
For use with high impedance circuit applications, however, they are not so good, as they draw appreciable current and therefore alter the voltage being measured.
They can be used to test residual-current devices (GFCIs) because the current drawn trips most RCDs when the solenoid voltmeter is connected between the live and earth conductors.
The continuity light displays if the contact is closed, and the solenoid voltmeter shows voltage presence if open (and energized).