The type of Christmas card known for its intricate design and often incorporating 3D elements like paper cutouts is called a "pop-up card." These cards feature detailed, elaborate designs that spring open into three- dimensional scenes, creating a visually stunning effect that stands out from flat cards. Popular themes include Christmas trees, snowmen, Santa Claus, and other festive shapes that fold out to form a layered and sculptural appearance when the card is opened. Pop-up Christmas cards combine artistry with surprise, turning a simple card into a little work of art that transforms flat paper into a captivating 3D display. They enhance the festive spirit by creating an engaging experience for the recipient, who sees the scene "pop up" as the card opens. This kind of card is often made by cutting and folding paper intricately to produce detailed figures that emerge from the card's surface. These designs can include multiple layers and elements such as folded triangles for trees, paper angels, or gift boxes, crafted from colored papers and sometimes glitter sheets, making each card unique and personalized. The 3D effect provides a tactile and memorable holiday greeting compared to traditional flat cards. Thus, the term you're looking for is "pop-up card," specifically known for its intricate, three-dimensional paper cutout designs in Christmas cards.