Variable Fonts technology allows users to navigate between two or more specific styles (called masters or sources) with high precision and much smaller font file sizes than several static fonts.
They do so on what is called a variation axis, which allows a continuous interpolation of outlines between compatible sources. It is a trajectory between different states of a given shape.
For example, the weight axis would shift points to adjust the stem thickness, allowing a transition from Thin to Bold.

FONT ENGINEERING ADVICE

The OpenType Specification defines 5 standard axes: weight, width, optical size, italic, and slant — italic being a link between two styles rather than an actual variation axis. These guidelines serve as reference for how these axes should be implemented.

The variations axes are defined in several font tables: the avar, the fvar and the STAT tables.