Ok but still, why test between 2 conductors? Why not test each individually?
As a few others have already said, what you measure is voltage
difference. The good example from above is a battery, it will do nothing unless you have contact to
both terminals.
But as with many things, you can define a point to be something, and measure relative to that to have some absolute (rather than relative) measure. For electrical power we
define the Earth (i.e. our planet) as being at 0V and then we can reference anything with respect to that arbitrary point. A Martian might find our planet is at a different potential to Mars, but we don't care as all we are doing is working here on Earth.
Now the difference between a battery and the AC power system is that in almost all cases, we take one of the live conductors (i.e. those carrying current) and reference it to the Earth through some conductive path, usually an earth rod or mat at the generator or substation. The live conductor we chose to reference to E we call
neutral as normally it has very little voltage on it, all of the others we call
line and for the typical UK system we have a nominal 230V L-N and 400V L-L (the physical diagram of the generator in post #10 helps explain the 1.73 ratio).
When you are "proving dead" you absolutely
must not assume anything about the wires in front of you. They may not have been connected/colour-coded correctly and/or they may be subject to a fault, and if you make a mistake it will be a doctor proving you are dead!
This is why you must follow the correct procedure for proving dead before any work, and you will automatically fail any practical exam if you don't. So you check from each conductor to every other conductor (and maybe to any metal work if the CPC is not already connected to it) to see if
any combination could prove dangerous, not just the L you might expect. If you have a total of X conductors you have X*(X-1)/2 combinations to check, which works out as 3 for single phase (L+N+E) and 10 for most three-phase (3L+N+E) systems.
You can get no-contact voltage indicators which work by looking for electrical fields around the conductor. While these have some uses, they are
not acceptable for proving dead as there can be situations when they do not reliably indicate voltage differences, and other cases when they incorrectly show a live conductor due to capacitive coupling from another cable ("phantom voltage"), a problem you also get with digital multi-meters due to their high impedance (hence very little current needed to register a voltage).