Hanukkah (“dedication” in Hebrew) commemorates the rededication of the Temple in Jerusalem by the Hasmoneans (Maccabees) in 165 BCE. Until the 20th century in America, Hanukkah was a very minor holiday with few specific dishes. Indeed, until the 14th century, there were no records of any traditional Hanukkah dishes. Then two types of foods emerged -- fried foods and dairy foods.
Fried foods, associated with the lighting of the menorah (candelabra), became the principal type of Hanukkah fare. Dairy and, in particular, cheese, emerged due to a misunderstanding of one of the books of the Apocrypha, Judith. The text, composed around 115 BCE, tells of Judith, a young widow from a town besieged by the Babylonians, infiltrated the enemy camp, fed the commanding general salty cheese to induce thirst, plied him with wine to slack his thirst until the general fell into a drunken stupor, then cut off his head with his own sword. In response to the loss of their leader, the enemy army panicked and fled. The timing of this story actually predates the Seleucid period by four centuries, but during the Middle Ages, when Jews no longer possessed the original text of Judith, the oral tale became associated with the Hasmonean revolution and Judith became variously the aunt or daughter of Judah Maccabee.
Sephardim typically prepare various rudimentary doughnuts (bimuelos and loukoumades) and fried pastries, such as shamlias (fried dough strips) and zalabiya (batter poured into hot oil in a thin spiral, similar to Amish funnel cakes, and coated with syrup or honey). North African Jews enjoy debla, dough rolled to resemble a rose, deep-fried and dipped in sugar or honey. Italians honey-dip deep-fried diamond-shaped pieces of yeast dough called frittelle.The Bene Israel in India prepare milk-based fried pastry called gulab jamun.
Among Ashkenazim, the fried role was eventually filled by blintzes, doughnuts, and especially latkes (pancakes). The original latkes were made from curd cheese, fulfilling the two predominant Hanukkah culinary customs in one dish. However, northern Europe had little oil available and, therefore, pancakes were typically fried in schmaltz (rendered chicken fat), which led to buckwheat latkes and, in the mid-19th century, to the now iconic potato latke.
A less well known Eastern European dish was ritachlich (grated black radish fried in schmaltz). In the 20th century, the Polish jelly doughnut (ponchik) made its way to Israel, taking on the Hebrew name sufganiyot, and it subsequently emerged as the most popular Israeli Hanukkah food, sold throughout the eight-day festival at almost every bakery and market. Dairy noodle kugels, cheese dumplings, cheesecakes, and rugelach also became common Ashkenazic foods for the festival. Russian Jews serve barley soup with sour cream, while Hungarians might offer some delkelekh (cheese buns).
As with other holidays, seasonal fare became traditional Hanukkah food. Historically, all unnecessary domesticated animals, generally males and older females past their reproductive period, were slaughtered before the onset of the winter and the resulting need to expend vital resources to feed them, corresponding to Hanukkah. Geese were the predominant fowl of western Ashkenazim, with many families keeping at least a small flock to provide eggs and occasional flesh, generally only eaten at special occasions. In Eastern Europe, this role was replaced by cattle and, since most Ashkenazim could at best afford the tough, inexpensive brisket, it became in many Ashkenazic households the traditional Sabbath Hanukkah food. In America, brisket garnered interesting variations, including onion soup mix, pineapple, cranberries, and cola. As you can see, food does not remain static.