A food that many people might know of is tteokjuk a rice cake soup that web eat on NewYear's day. The reason that we eat tteokguk on this day is it represents long life and purity. The stick of rounded rice cakes in tteokguk also represent wealth and good fortune.
You may also have hear about songpyeon. It is a half moon shaped rice cake that we eat on Chuseok or Korean thanksgiving day. It represents hope for a better future.
Finally, we eat patjuk, an adzuki-bean gruel in Dongji which is the Korean celebration of the Winter solstice. The custom of eating patjuk on the winter solstice came from folk beliefs. In particular, color of patjuk is
thought to repel bad energy and prevent the spread of infectious disease.