Originally to ‘proof’ something was to check it for quality. Medieval armorers would proof armor by firing crossbow bolts at it. Later on, early guns were proofed by overloading them and firing them to make sure they would not blow up. gunpowder was checked for strength and lack of dampness with various devices that measured the result when you ignited a charge.Proof is also a measurement of alcohol (either by volume ABV or by weight ABW) content in a spirit.
This is now usually done with a hygrometer to determine the specific gravity of a fluid and this will give you a result. This is also somewhat boring compared to how it used to be done and is still used in some parts of the world because of either: 1. lack of equipment, 2. because it is fun. I am referring to setting fire to the whisky, with or without some explosives to boot.
In England and America, the old method was to mix the spirit to be tested with gunpowder and then set alight. If it was over 100 proof (50% alcohol or more) it ignited. If it merely wet the gunpowder down so it would not flash it was less than 100 proof or more water than flammable alcohol.
In Russia the way distillers of Samagon (bootleg vodka) test their spirit (or convince buyers) is to put a match to it and see how well it burns (if at all). if you have a clear blue flame it is 100 proof or more and good quality, yellow flame or oily smoke is not a good sign. A further method of testing ( for high proof) is to put some whiskey in a small bottle and shake it. If it beads, and how large the beads are will tell you the proof.