The term ombré comes from French and simply means shaded: when applied to a dial, it indicates a gradual color transition, usually from the center towards the periphery or vice versa. It's not a modern invention. I remember from my bench dials from the Sixties and Seventies — Longines, Zenith, certain Rolex sports models — where the painted base darkened at the edges without anyone attaching a specific name to it. Today the term is everywhere, but the technique remains the same.
The most common execution in contemporary watchmaking is concentric lacquer: you start with a base completely painted in the chosen color, then you spray black lacquer in concentric passes towards the edges, increasing the density to achieve the desired gradient. Rolex uses exactly this method on its lacquered ombré dials: green, burgundy, salmon — at the center the color is saturated and clean, at the edges it shifts towards deep black. The final effect can evoke a sunset sky or the bottom of a wine glass, depending on the starting color.
A variant is the so-called fumé dial, where the shading starts from a lighter, almost transparent center and darkens towards the periphery. Technically it's the same principle inverted. In certain manufactures the two terms are interchangeable, in others they're not: Rolex tends to use ombré for colored lacquers, fumé for smoked sapphire crystal dials. It's worth keeping them distinct because the manufacturing process is different.
There are also alternative optical approaches. The Dietrich SD-1 overlays a transparent sapphire disc with indices printed on the back over a shaded base underneath: light passing through the crystal casts real shadows on the lower dial, and the effect changes with the angle of illumination. It's not ombré in the strict sense, but it works on the same visual principle — perceived depth through the interplay of light and color. Certain dials with numerals printed on the inner side of the sapphire crystal also exploit this logic.
From a legibility standpoint, ombré is a choice with a cost: the contrast between indices and background varies depending on which zone of the dial they fall into. At the center it may be perfect, at the edges the added black can reduce distinction. It's a compromise that every designer must consider before signing off on the design.