Furoshiki is a traditional Japanese wrapping cloth that came into use during the Edo period (1603-1868); it was used in public bathhouses for spreading on the floor while undressing and for wrapping bathing articles. Today, furoshiki can be used to wrap gifts, serve as a tablecloth, as a decoration on a wall, etc...
The Ministry of the Environment Government of Japan has created a handy illustrated guide on using furoshiki for wrapping gifts.
Link | PDF guide