Why waste paper, tape and ribbons to wrap gifts when you can just use fabric, or furoshiki cloth?
Furoshiki is the art of wrapping something in fabric, and it's also the word used for the cloth itself. In Japan you can buy "furoshiki cloth," but really you can use any square or rectangle piece of fabric you have lying around.
From Lifehacker:
The word furoshiki (風呂敷) refers to the craft in addition to the cloth itself, which is usually decorated with a colorful design. It roughly translates to "bath (furo) spread (shiki)" because the cloths were originally used to carry items to the public bath house and then used as a kind of bath mat. Nowadays, it's just a clever way to wrap up and carry bottles, food, gifts, and other items.
Here are more furoshiki 101 videos to check out: