Nagaimo originated in China, and it was cultivated in Japan around the 17th century. Naga (long) imo (yam) is as long as its name, measuring from 12″ to 40″. However, it is usually cut in smaller pieces, packaged and sold at markets.
Nagaimo is often eaten raw, though that is rare for yams. Grated Nagaimo is called “Tororo” and used in dishes like Tororo with rice or Tororo with soba. Tororo has a very viscous texture (some might even call it slimy), so that it sometimes functions as a thickening agent in some recipes such as Okonomiyaki.
You can find Nagaimo at Japanese markets in the produce aisle.