From the website by the same name:

Furoshiki is a type of traditional Japanese wrapping cloth that was 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 sento (public baths). Before becoming associated with public baths, furoshiki was known as hiradzutsumi, 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.