When using a multimeter to test for continuity, it should be set to measure resistance (in ohms). When it displays a reading of zero, it indicates continuity (no resistance or "opens" in this circuit).

A broken or discontinuous circuit will have an "infinite" resistance reading.

A bad connection, a partial short, or a component in the test path will cause a reading somewhere in between zero and infinity.

A test for resistance will not indicate whether or not current is flowing, and current in a circuit being measured for resistance could damage the multimeter. Always make sure all power is removed from a circuit before measuring resistance.