tl;dr: it’s totally arbitrary.
The way they used to make wire was to start with a bar of metal and run it through a set of pinch rollers to make it smaller. One set of rollers can only reduce the size of the metal so much, so they run the metal through a series of rollers until it’s down to the thickness you want. The number of rollers you go through is the gauge. The more rollers, the higher the gauge, and the thinner the wire.
That’s a terrible way to measure things, especially since each manufacturer had their own rollers and so the gauge depended on the maker. Eventually a standard was defined (American Wire Guage; AWG) and you can see it on this [chart](https://www.rembar.com/resources-technical-information-on-refractory-metals/american-wire-gauge-awg/).
There are other “gauge” measurements and they’re all just as arbitrary. Examples include how far the rails on a railroad track are (4’8.5″ in the U.S. and England), or the diameter of a shotgun barrel as /u/The Jeeronian has described.
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