Woodcut or Woodblock Printing
Woodblock printing, on fabrics, was practiced by the Egyptians at least four thousand years ago. However, it wasn't until the 7th century, in China, that printing on paper became common. In the 8th century woodblock printing was introduced into Japan, but it wasn't until the mid-1600s that multiple color printing was perfected (before that time, black and white prints were hand-colored by brush).
To create a woodblock print, designs are drawn on blocks or planks of wood (almost any wood can be used but fine grain woods such as cherry or basswood are preferred). The parts not to be printed are carved away, leaving a design in relief. A different block of wood is carved for each color to be printed. Ink is applied onto the carved block and then paper is placed on top and burnished with a baren (a Japanese tool for hand printing), transferring the raised design onto the paper. Traditional Japanese woodblock prints are printed by hand and use only watercolor inks (normally hand-ground powdered pigments mixed with water) and rice paste (as a binder) on handmade hosho (paper hand-made from the inner bark of the mulberry tree). One color is printed on all sheets to be printed and then the process is repeated with each block until the all the colors have been applied. It can take a month or more to print complex prints.
Western-style printing, using oil-based inks, presses, and machine-made paper, evolved from these early techniques. While traditional Japanese woodblock prints were not editioned, today woodblock prints are normally produced in editions, limited in number as indicated in pencil below the image. The notation 1/30 means that this particular print is number one of 30 in the edition. By signing and numbering it, the artist is guaranteeing that there are only 30 original woodblock prints of this design, although there may be some small number of Artist's Proofs. The use of the term "state" after an edition number normally signifies that there are prints using the same design but printed with a different color scheme.
For a more visual demonstration, please see "What is a Print", an informative description from the Museum of Modern Art in New York City.