The eight-day festival of Hanukkah commemorates the Miracle of Oil -- honoring a flame that miraculously burned for eight days. To celebrate, Jews all over the world eat foods fried in olive oil. Hanukkah falls at the end of the oil-pressing season, so olive oil was always readily available.
Nobody is exactly sure why latkes ended up as the traditional food for this holiday. However, most traditions have modest beginnings. Potatoes were cheap and usually the only food in the root cellar during cold winters.