"Origami" is the traditional Japanese art of paper folding, which started in the 17th century AD and was popularized in the mid-1900s. It has since then evolved into a modern art form. The goal of this art is to transform a flat sheet of material into a finished three dimensional object through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami.
"A thousand cranes" is a group of one thousand origami paper cranes held together by strings. An ancient Japanese legend promised that anyone who folds a thousand origami cranes will be granted a wish by a crane, such as long life or recovery from illness or injury. In Japan, it is commonly said that folding 1000 paper origami cranes makes a person's wish come true.
Today, it is a common gesture for Japanese to send a thousand cranes to people who are suffering from illness or injury and to those who are having a difficult time in their life, wishing for their fast recovery.