"Furoshiki (風呂敷, furoshiki) are a type of traditional Japanese wrapping cloth that were frequently used to transport clothes, gifts, or other goods. Although possibly dating back as far as the Nara period, the name, meaning "bath spread", derives from the Edo period practice of using them to bundle clothes while at the sentō (public baths;public furo). Before becoming associated with public baths, furoshiki was known as hirazutsumi (平包), or flat folded bundle. Eventually, the furoshiki's usage extended to serve as a means for merchants to transport their wares or to protect and decorate a gift.
Modern furoshiki can be made of a variety of cloths, including silk, chirimen, cotton, rayon, and nylon. Furoshiki are often decorated with traditional designs or by shibori. There is no one set size for furoshiki, they can range from hand sized to larger than bed-sheets. The most common sizes are 45cm (17.7 inch) and 68-72cm (26.7-28.3 inch).
Although there are still furoshiki users in Japan, their numbers declined in the post-war period, in large part due to the proliferation of the plastic shopping bag. In recent years, it has seen a renewed interest as environmental protection became a concern. Furoshiki are, however, commonly used to wrap and transport lunch boxes (bento) and often double as a table mat for the lunch."
Yami also sent me this link diagramming how to do this.