A die-cut business card is cut into a custom shape — rounded corners, a notch, or an entirely custom silhouette — using a specially made cutting die, rather than the standard rectangle.
A distinctive shape can make a card memorable in a stack of conventional ones, and works especially well when the shape relates directly to the brand (a leaf-shaped card for a landscaping business, for instance).
The practical trade-off is storage: non-standard shapes and sizes don't always fit neatly into standard card holders and wallets, which is worth weighing against the novelty value before committing to an unusual cut.