The leaf business card is one of many unique card shapes you could use for your business. The name comes from the two rounded opposite corners added to a regular rectangular business card, that give it its distinct leaf shape.
The unique shape of leaf business cards, as well as the shapes of other die-cut business cards, come from the die-cutting process. A die is a specialized tool used to cut or shape paper and other materials. Think of a die as a cookie cutter that you can use to create the shape that you want for your business card and other printing materials.