Wire gauge is an imperial measurement of thickness of wire. Same as wiring in your house. Smaller number is thicker. 12g spoke is thicker, heavier than 14g. 12/3 house wire is thicker, heavier than 14/3 wire. Wire gauge is used in many engineering fields. The g stands for gauge. Also expressed as AWG, American Wire Guage.
Sheldon Brown can help with all manner of wheel building.
That dollar reference book at the home store has this table. Pocket Reference by Thomas Glover. There are American and British wire gauges, a little different, and a steel plate gauge. I don't know which one the bike industry uses. Most bike parts originally came from Britain, so possibly that one.
Thicker spokes have lower gauge number. There is no easy way to mentally convert gauge # into mm, and for most people there isn't much need to remember the exact thickness in mm, either.
Similar system is used in electrical wire, but wire gauge numbers correspond to different thickness, i.e. wire #14 and spoke #14 are not same thick. At least, in the US they are not.
I think this is how the diameters go.
12G 2.6mm
13G 2.3mm
14G 2.0mm
14G spokes are used on most bicycle wheels, and 12G is used on many ebike hub motor wheels. Sometimes 13G is used. A few use 14G. Big discussions in other forums on which is preferred.
14G spokes are used on most bicycle wheels, and 12G is used on many ebike hub motor wheels. Sometimes 13G is used. A few use 14G. Big discussions in other forums on which is preferred.
There are fancier butted spokes as well, which are thicker at the ends. I built my current wheels with DT Alpine III spokes, which are 13G at the head, 15G in the middle, and 14G at the threads.
They are thickest at the head where spokes are most likely to break. They are thin in the middle which makes them lighter, and also makes the spokes more elastic, which contributes to a wheel that stays true. Then back to thicker at the threads for strength.
I used Saphim Strong spokes, which are 13G at the motor end, and 14G down at the rim for my 20" wheels. Not only more durable, but thicker spokes would have been too stiff to thread around the other spokes as the pattern fills out. This is more of a problem when the spoke length is short. Happens with big motor on a 26" wheel or any motor on a 20" wheel.
A spoked wheel is meant to be elastic, to offer some flexibility and suspension. That's why you don't see mag/solid wheels (generally) on off road bikes/motorcycles.