Measuring voltage is measuring the potential difference between two points. If you measure an intact fuse, there is zero potential difference between the two probes of your meter and therefore the difference (voltage) reads zero on your meter.
This is the same as measuring two points on the same live cable. There is no difference so no voltage is measured. However, if you measure between phase and neutral you will see a difference. In a 230VAC T-N-C-S system, the phase is at 230V potential whereas the neutral is bonded to ground at the incoming supply and therefore has 0V potential. The potential difference between phase and neutral is 230V and you therefore measure 230VAC on your meter.
This is similar to your blown fuse situation. Think of the incoming side of your fuse as the phase at 230V or whatever voltage your system is at. The load side of your blown fuse now has the same potential as your neutral which is 0V in most cases. So, if you measure across a blown fuse you get 230V.
If you measure between neutral and earth (ground) in a T-N-C-S system, you should also get 0V on your meter as these are connected together at the incoming connection as mentioned previously.
Let’s say you have an old appliance that is not connected to a GFCI (RCD) and it has a short circuit to earth in it. If you were to measure the frame of the appliance to earth, you will get something close to 230V, and that is where the danger comes in. There is now a potential difference between the frame of your appliance and earth, and if someone completes that circuit, with their two arms for example, their left arm will be at 230V and their right arm will be at 0V and they will get a shock across their chest (most dangerous kind of shock).
The people saying that electricity flows through your voltmeter are incorrect. A voltmeter is high-resistance/impedance to prevent electricity flowing through it. If electricity flowed through your meter when you connected your probes, you would have a big problem i.e. a short circuit.
They may be confusing a voltmeter with an ammeter which measures current. An ammeter has a low (close to zero) resistance/impedance because it NEEDS the electricity to flow directly through it so it can show how much current is flowing in the circuit.
Not exactly ELI5 but hopefully makes sense.
Source: Am trade qualifed Electrician
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