A die is cut to the shape, heated, and pressed against the paper with a sheet of metallic film sandwiched between them. The heat melts the film's adhesive layer onto the paper; the rest of the film peels away, leaving just the stamped shape. Beyond gold and silver, foils come in holographic and colour finishes too.
CMYK and spot inks are just pigments absorbing and reflecting light — no matter how bright, they can't produce actual sparkle. Foil leaves real metal particles on the surface, so light bounces differently depending on the viewing angle — the fundamental difference between a "metallic" gradient on screen and real foil in hand.
Combined with embossing (→ emboss-deboss), the same die adds shine and depth at once, which is why the two so often ship together on premium pieces. The catch: cutting a custom die is expensive, so foil stamping gets much less cost-effective at low print quantities.
When to use
Best as an accent on a simple logo or pattern. Die costs make it expensive at low quantities (tens to a few hundred pieces), so confirm the print run size before committing.