Gauge is a measurement of diameter of a wire. It’s also refereed to as AWG (American Wire Gauge).
Simply put, the bigger the number, the thinner the wire.

For making jewelry, the most common gauges are 16 to 26 gauge. Earwires are usually 19 to 22. Hoop and Kidney earwires are mostly 23 ga as they are hard wires. Pins are usually 24 gauge. High-cut gem stones and pearls have smaller holes so you may want to use 26 ga to be safe.
Gold filled findings are thinner as they are harder to bend.

An easy way to measure the gauge of wire is to put 10 pins/earwires together on the same surface; measure the total width and devide it by 10.

Hope this information is helpful when you choose gauge size for your wire, earwire, and pins.
Here is a conversion table.