Meibutsu (literally, "famous thing"), is the concept in Japanese culture that every municipality, from the largest city to the smallest town, needs to have a famous food or dish, which can be anything from loaches to apples to noodles to dumplings, and everything in between.
Meibutsu serve an important function in Japanese society, because whenever Japanese people go on a trip to another part of Japan, whether it be for business or pleasure, they are expected to bring back omiyage for their co-workers, and the easiest, most convenient, and therefore most common thing to do is to buy whatever the local meibutsu is.
The average Japanese person has a surprisingly detailed knowledge of what the various meibutsu are for a wide assortment of cities, towns, and other locales across Japan, gained through their own travel, tasting the omiyage brought back by their co-workers, and through ubiquitous programs on Japanese TV in which marginally famous celebrities are dispatched to various parts of Japan to sample the local meibutsu.
This means that it is really hard to fake people out by giving them the wrong item, if you forgot to buy the actual meibutsu, which has led many of the larger train stations and airports to stock a wide variety of authentic meibutsu from all over Japan in their gift shops to let returning travelers who forgot to buy enough omiyage in the actual place to have a second last chance to buy it before they have to face their colleagues the next morning. This is technically cheating, but almost everyone does it from time to time.
The various meibutsu are always marketed as ancient and traditional local delicacies that were always eaten in that region, but many meibutsu are of much more recent origin. Although it is true that regional variations in cuisine always existed in Japan, the concept of meibutsu was not really developed until the tourism industry first started to get going in Japan during the mid Edo Period. With the daimyo lords required to travel to and from Edo every other year as part of the sankin kotai system, a vast amount of shops started springing up along the major highways, particularly the Tokaido, which was the main road to Edo, where merchants would hawk local delicacies. Soon word of particularly delicious or exotic local cuisines began to spread around Japan, and the concept of meibutsu gradually developed.
But even into the 20th century, many towns still had the same meibutsu as the next town over, or even no meibutsu at all. But in the 1950s and 1960s, however, as travel around the country became easier and more common for many ordinary Japanese, towns became increasingly aware that it was really important to have one's own special meibutsu, and to somehow distinguish your meibutsu from that of neighboring towns, as a crucial part of your package for marketing your town as a tourist destination. By the 1970s and 1980s, every town had its own meibutsu, which they marketed heavily in travel literature produced by their tourism bureau, even if they had had to pretty much make it up out of whole cloth.
Some Famous Meibutsu:
Note that the term "meibutsu" can also have a more expansive meaning which includes local handicrafts, such as porcelain dolls from Fukuoka, lacquerware from Nara, swords from Kamakura, etc., but when used in isolation without further explanation, the term almost always refers to food.