A die — a metal plate carved with the shape — presses into the paper under pressure, permanently raising it (emboss) or pressing it in (deboss). No ink is involved; the shape reads purely from touch, or from light raking across the surface at an angle.
Because it's perceived entirely through the shadow and highlight created by the paper's own contour, the same emboss can look completely different depending on where the light comes from. That's why photographing or simulating it with the light source slowly shifting sells the depth far better than a flat, evenly-lit shot.
It's frequently paired with foil (→ foil-stamping) — "emboss plus gold foil" shows up constantly on premium business cards and invitations. An emboss used entirely on its own, with no ink at all, is called a blind emboss.
When to use
Works best on simple, bold silhouettes like a logo mark or pattern. Avoid fine print or thin hairlines — the paper can tear or the impression can blur out.