While Wikipedia quotes it as being "a food item that is considered highly desirable in certain cultures," what they really mean is that it's panned by most of the population, but more people in that country will eat it than anywhere else.
A delicacy can range from poor people food (like the natto parents will force their children to eat), to tiny portions of overhyped rich people food (like french truffles).
Other delicacies are used purely for novelty & entertainment value outside their country of origin, such as eating a can of Surströmming, Balut, Pidon, or drinking Birds Nest Soup for a web review series about gross foods.
Cow-TONGUE, Cat-Penis, Dogs-Balls, Pig-Ears & Feet, etc.
Cow-TONGUE, Cat-Penis, Dogs-Balls, Pig-Ears & Feet, ...see Chinese cuisine for more details of disgusting 'food' ideas, they eat any living thing.