Motsunabe is a nabe dish made from Motsu (offal).
A pot is filled with soup and prepared beef (or pork) offal and boiled until the offal absorbs the soup; cabbage and Chinese chives are added, and eaten when ready. The base soup is usually soy sauce with garlic and chili pepper or miso. Champon noodles are usually put into the pot and boiled to complete the dish after you eat the offal and vegetables.
In Motsunabe served in restaurants, beef intestines are mostly used, but various kinds of offal can be used, considering the name of Motsunabe. Actually, Motsunabe dishes made from many kinds of offal besides intestines are not unusual.
Motsunabe originally was a local dish around the Fukuoka City area. As some local restaurants expanded their business to Tokyo in about 1992, right after the collapse of the bubble economy, Motsunabe was taken up by the media; as a result, it became a boom, with its advantage of low price and being a good match for Japanese sake, and came to be known nationwide. However, it didn't take root in big city areas like Tokyo; part of the reason was that there was a BSE issue and also the popularity was just temporary.
In the Kansai area, though, it has taken root as the forms of Horumonyaki (grilled beef or pork offal) and Horumonnabe (beef or pork offal cooked in stock), which are different from the Motsunabe of Hakata, Fukuoka Prefecture. And, since the 'Mini-bubble economy' in about 2006, it has been gaining popularity again in the Tokyo area.
In Fukuoka, having nothing to do with the dropping popularity in the Tokyo area, it still remains popular after being affected by the BSE issue; there are many Motsunabe restaurants of long standing, and it is the second most popular dish, just behind Hakata ramen (Chinese noodles) in general izakaya restaurants.