The question, "What is fondue?" has a surprisingly complicated answer. In its simplest and purest form, the modern word means a dish in which small pieces of bread are dipped into melted cheese using skewers or forks. In the latter half of the 20th century the word became generalized to have other similar meanings, such as a sweet dish involving pieces of fruit dipped in chocolate or another variation where meat is actually cooked by being dipped in hot oil.
Unfortunately fondue has become so closely identified with the 1960s and '70s that many people mistakenly think it was invented by trendy college students. This is a shame for two reasons. First of all, this dish is wonderful and should not be sneered at for any reason. Second, it's simply wrong. Fondue has a long and illustrious past that extends far beyond its modern associations.
Events in culinary history are seldom noted by historians, so it is impossible to point to a single moment when the dish was invented. The situation is complicated by the word's ambiguity in a historical context. There were recipes for preparations involving cheese melted in wine in German cookbooks as far back as the late 17th century, but they were called by other names. We can only say with certainty that by the 1730s, French cookbooks were including recipes that were actually called fondues. However, the widespread popularity of the dish in French cuisine, and arguably the beginning of the world's fascination with it, probably can be attributed to an 1825 cookbook by Jean Anthelme Brillat-Savarin.
Ironically, this documentation still does not give us a satisfactory answer to the question, "What is fondue?" Brillat-Savarin's recipe is something quite different from the modern meaning of the word. It includes eggs as well as cheese and is closer to what we would call a soufflé today.