It's a mapping of the rectilinear Cartesian coordinate system. Just as a semilog graph paper distorts the X/Y plot to (perhaps) simplify a curve, and moves '0' infinitely far to the left, so one can replace the vertical grid with circles all tangent at one point (which represents infinity...), and the horizontal grid with circles all passing through that point, and everywhere intersecting the 'vertical' circles at right angles...
This mapping, oddly, preserves angles and intersections, and is a perfectly acceptable model for 'line', 'point', and all the other elements of Euclidean geometry.
The classic Smith chart is mapped with the center of the unit circle at impedance match, the horizontal diameter indicating purely resistive impedance, and the 'arc' grid, all arcs that are perpendicular to the unit circle, represents addition of inductive or capacitive impedance.
The circles and arcs are the coordinate system that locates the complex impedance, Z =3D R + jX, the circles being constant R and the arcs being constant X.