The gauge is how thick your jewelry is. Jewelry gets thicker the smaller you go in numbers. For example, an 18 gauge nose stud is thicker than a 22 gauge nose stud. You will see gauge written like this: 16G, 16g, and 16 gauge.
If you don't know which gauge you wear you may be able to measure it at home!
As long as you are wearing the correct gauge of jewelry in your piercing, just use a caliper to measure how thick (big around) your jewelry is. For reference, a "normal" ear lobe piercing that has not been stretched (especially if it was done with a piercing gun) is 20 gauge.
AWG (American Wire Gauge) Measurements:
22 gauge = 0.64mm
20 gauge = 0.81mm
18 gauge = 1.02mm
16 gauge = 1.20mm
14 gauge = 1.63mm
12 gauge = 2.06mm
10 gauge = 2.59mm
8 gauge = 3.25mm
The millimeter measurement that corresponds with each gauge can vary slightly depending on the manufacturer (usually +/- 0.5mm). For example, you may find that your 16 gauge helix stud measures 1.3mm.