A vernier scale lets one read more precisely from a measurement scale. It was invented in 1631 by the French mathematician Pierre Vernier (1580-1637). In some languages, this device is called nonius, which is the latin name of the portugese astronomer and mathematician Pedro Nunes (1492-1578).
Verniers are common on sextants, machinists' measuring tools (all sorts, but especially calipers and micrometers) and on slide rules.
When a mechanical measurement is taken, an index lies at the true datum of the measurement. This will usually be between two gradations of the data scale ("fixed", in the diagram). The indicating ("vernier") scale is used to provide additional precision without resorting to estimation.
The indicating scale is constructed with its zero point coincident with the index of the data scale. Its gradations are at a slighty smaller spacing than those on the data scale: N gradations of the indicating scale would cover N-1 gradations of the data scale. The indicator scale measurement corresponding to the best-aligned pair of indicator & data gradations yields the additional precision.
On instruments using decimal measure, as shown in the diagram, the indicating scale would have 10 gradations covering the same length as 9 on the data scale. Note that the vernier's 10th gradation is omitted.
On an instrument providing angular measure, the data scale could be in half-degrees with an indicator scale providing 30 1-minute gradations (spanning 29 of the half-degree gradations).