Gauge is simply the diameter of the string in millimetres. Our 120 strings run from 1.18 mm to 1.35 mm, median 1.25 mm. 10 are 1.20 mm or thinner, 84 sit in the 1.21–1.28 mm band that dominates the market, and 26 are thicker than 1.28 mm. American packaging often prints a gauge number instead — 16 is about 1.30 mm, 17 about 1.25, 18 about 1.20.
Thinner string bites the ball more, because there is less surface holding it and the mains slide and snap back more freely. It also feels softer at the same tension, because there is less material to stretch. Both of those are why players chasing spin go thin.
The cost is durability, and it is not marginal. A 1.20 mm polyester in an open string pattern can break in a couple of hours for a hard hitter; the same string at 1.30 mm may last several times as long. If you are breaking strings weekly, going up a gauge is cheaper than going up a brand.
The other half of the decision is your string pattern. An open 16×19 saws through thin string; a dense 18×20 protects it. So a 16×19 player who breaks strings should go thicker, and an 18×20 player who wants more spin can afford to go thinner without paying for it every fortnight.
If you have no idea and want one answer: 1.25 mm — the median of our whole catalogue, and the gauge most manufacturers treat as their default. Move down for more bite, up for more life, one step at a time.