Digital multimeter - Continuity mode/setting
General
Be wary of the 'continuity' mode. It is not a short-circuit indicator. For example, if I use the 'continuity' mode of my multimeter to measure a good 56 ohm resistor from my spares box, my multimeter will beep. That is because the 'continuity' mode of my multimeter beeps at anything under 100 ohms. So, the beeping of continuity mode needs to be thought of as a low-ohms indicator. Some things that you measure are expected to be of low ohms. If measuring resistance, you really should have your multimeter in resistance mode (and then in measuring, knowing roughly what to expect).
What is the definition of 'continuity' ?
As far as I am aware, there is no international definition of 'continuity'. For example, for all I know, in the AC power generation/delivery industry, if a technician unexpectedly measures 3423 ohms between the primary and secondary windings of a HV (high voltage) transformer, he/she may declare that continuity exists.
The continuity mode of my multimeter beeps at anything under the value of 100 ohms. Other make-model of meters are known to use a different value.
An example of where I might use the continuity mode
I have a 200 foot long cable, a cable that has 150 wires in it. I need to verify that there are no breaks in any of the 150 wires. If I was to use the resistance mode on my multimeter, I would need to glance at my multimeter every time that I move the probes to a different wire. My job would be much easier if I didn't need to look at the multimeter. That's where continuity mode helps me. After I move the probes to a different wire, the beep informs me of 'continuity' in the wire.
The continuity mode works for me there because, on my multimeter, the mode beeps on anything less than 100 ohms, and I am expecting the resistance of each wire to be in the rough order of 5 ohms (for that cable).
However, if I needed to ensure that end-to-end, no wire measured more than 7 ohms, then the continuity mode on my multimeter is useless. For example, if a particular wire is 9 ohms, my multimeter would beep. For this task, I will have to use the resistance mode, and glance at the multimeter every time that I move the probes to a different wire.
When is it BEST to use the continuity mode ?
As far as I am concerned, there is no 'It is best to use continuity mode in situation XYZ.'
By default, use the resistance mode, and again, one needs to know roughly what reading/value is expected. Think of the continuity mode as an optional extra that can be helpful in some situations (such as the example I gave where it was helpful not to keep looking at my meter, and the expected ohms per measurement was within the 'beep' range of the continuity mode of my meter).
For example, if I am seeing if the metal frame of a floppy drive is adequately connected to the computer case, I would be worried if that connection measured say, 20 ohms. My multimeter, in continuity mode, is going to beep in that situation.