In Japanese culture, noshi is a decorative element attached to gifts. It can be attached to gifts for weddings, for births, and for other congratulatory events such as graduation or promotion. Noshi is given as a token of good luck; it is never used in funerals or burial ceremonies. [Photo from here]
According to Complete Origami (Eric Kenneway), attaching noshi to gifts has been a Japanese custom since the 12th century. He suggests that the earlier forms of noshi may have been fresh meats or fish but, with time, noshi evolved to include dried fish (specifically, stretched and dried abalone).
This is somewhat consistent with the information from Noshi: Classic Japanese Origami (Isao Honda), which states that "noshi" is an abbreviation of "noshi awabi" which literally means "stretched abalone".
As time passed, the meat/fish part of noshi became less prominent. In modern Japanese culture, a narrow strip of yellow paper is used to symbolize the stretched abalone. In some cases, a piece of paper with the words "noshi" written on it is used. Sometimes the strip of paper is replaced with seasonal flowers or pine needles. There are even some noshi which do not have the inner strip of material but retain only the formally-folded, outer wrapper. [Photo from here]
Currently, the term "noshi" refers to the folded paper which is attached to a gift as a sign of good fortune; the meaning and presence of the meat/fish is all but forgotten.
How to Fold Noshi
In the past, noshi was folded with two rectangular sheets of hosho (thick, handmade paper). The sheets (one red and one white) were placed one-over-the-other to achieve double-sided color.
In modern times, noshi is folded from a rectangular or a square sheet of paper. It can be two overlapping sheets of paper (one red, one white) or it can be one sheet of double sided origami paper (red and white). A fairly new invention is noshigami. There are even more modern iterations on the concept: there is wrapping paper with the image of noshi printed directly on the paper itself. The gift is wrapped so that the image of the noshi is on the top-right side of the package.
Noshi is folded in such a way that it has no internal locks. A strip of paper or decorative cord is used to keep the folds in place. The cord, called Mizuhiki, is a bundle of stiff string knotted in a decorative manner. The knotting of mizuhiki is an art form in itself and has symbolic meaning. More about mizuhiki here. [Photo from here]
Below are instructions on how to fold noshi. Please be aware that the method of folding was not acquired from those who are familiar with the age-old art of folding noshi. Indeed, most Japanese people buy pre-made noshi the same way an American may buy a pre-made gift bow from a department store. Click on the image for instructions.