Kirigami is the Japanese art of intricately folding and cutting paper into various 3D designs, not to be mistaken with origami, which is only folding paper. The general idea behind kirigami is to fold a piece of paper in such a way so that when you make a cut it will cut through many layers of paper, and create a design. A flower is a common design for kirigami, which is very similar to a paper snowflake. The word itself is composed of the words kiri, which is Japanese for cut, and kami, the Japanese word for paper. It is said that kirigami originated in China, where many people cut rice paper to create beautiful and elaborate designs. Currently, there are many different books and kits devoted to the art of kirigami that can be found in bookstores, and online.
Sources used:
http://www.bartleby.com/61/45/K0074500.html
http://cddart.vip.sina.com/index_e/paper.htm