Here are other definitions:
Wikipedia: Paper models, also called card models, “pepakura” or papercraft, are models constructed mainly from sheets of heavy paper, paperboard, card stock, or foam.1)
PaperCraft Museum: Papercraft is a hobby where computer images are printed, cut into pieces, and glued into a 3-dimensional model.2)
Wiktionary: The art of making things from paper.3)
As you can see, the word papercraft is quite vague, thus paper modeling is more commonly used to describe what is covered in this wiki. Indeed, as defined by PaperCraft Museum, one usually talks of papercraft as a hobby in which a printed template is cut into pieces which are then folded and/or glued together to form a three-dimensional model.
The earliest found representation of a paper model is a paper cross designed around 1529 A.D. by the German engineer Georg Hartmann. This sundial depicts the crucifixion of Jesus on the front and a miracle of Moses on the back. It is now located in the Germanisches Nationalmuseum in Nuremberg, Germany.4)
During World War II, materials were in short supply and metal was very rare, leaving toy makers the only option to switch to paper and wood. Books and boxed sets of paper models then became popular toys in the United States. Some models, like those by the Englishman Wallis Rigby, were even printed on the colored pages of newspapers.5) In the 1940s, Micromodels were very popular in the United Kingdom. They were miniature-sized paper models that could fit in a post card.6) Following the end of the war, the material stocks when back to normal and plastic models replaced paper models.7)
Since the popularization of the World Wide Web, it has become easier to access paper model templates. For instance, many blogs and message boards collect and share downloadable templates that are either scanned or designed with a computer. Indeed, anyone can now learn to self-create his or her own papercraft templates thanks to 3D modeling software and specialized papercraft creation programs like Papercraft Designer by Tama Software. These templates can then be printed using a printer.