The origins of origami are not known exactly but there are presumptions about the appearance of origami through Ts'ai Lun in China after the development of paper in 105 B.C.

Origami's name
In the early beginnings this art was called 'Orikata' (folded forms) and it was renamed to 'Origami' (Ori means to fold and Kami means paper) around 1880 from S. Konishi of the Ochanomizu Kindergarten. But the japanese word Kami is actually a hononym for god and spirit which would declare its religious nature.

Origami as decoration
Folding sheets of papers were reserved for specific ceremonies at the beginning because paper manufacturing was quite expensive at that time. White sheets of paper were not only used for decorate for example the Shinto temple but also of some visitors which stuck themselves tiny pennants in their hairs and small pupae were used for religiose rituals. These ways of decoration and using folded sheets of paper have been used over many centuries and weren't changed.

Written records of origami figures
Unfortunately there are no chinese records of folding origami available. The oldest japanese notes, hovever, date back to the 18th century and because of that many historians even maintain that origami is a japanese development definitely. Nowhere else is the art of paper folding more fostered and nourished than in Japan.
First origami was only used as writable base for religious ceremonies, later it was disposed for decorating houses and for folding usefull objects for the kitchen (for example a drinking cup) but also for amusements.
The folding techniques could be quite difficult at that time already. Therefore people either have retained one or more examples of each origami figure or have marked each folding with pinpricks on sheet of papers and were passed down generations but unfortunately by oral traditions so that only the easiest figures were preserved.

Spread of origami
After the paper manufacture had spread also in europe at 751, a european tradition delevoped too. The creation of representive figures was forbidden to Arabians who followed their bents for maths and geometry therefore. Spanish explored geometric stuctures and developed 'Papiroflexia'. Germans started folding napkins as table decorations which could be quite complicated.
However, origami made a right breakthrough first during the nineties after different books have been published with numerous instructions.