From Smithsonian:
My Italian grandfather was known to eat a lot of strange things: pickled eels, tripe and anything slimy that would be considered disgusting to most children. For New Year’s Day his favorite food was a giant gelatinous sausage called cotechino, cut into sections and smeared with mustard. My brother and I joked that the sausage must have been made from the worst of the pig, like the eyes.
As an adult, I developed a taste for cotechino (which contains plenty of pig fat, but no eyeballs), and have learned that this delicacy, and pork in general, is often considered a propitious food to eat at the beginning of the year. Many of our holiday customs go back to when we were an agrarian society. “In many parts of Europe, pigs were easier to grow than cows because they take up less space and eat anything,” says Janet Chrzan, a nutritional anthropologist at the University of Pennsylvania. “And pigs were slaughtered around the time of the winter solstice.” Food has always been a powerful symbol, especially during rites of passage, such as the start of a new year. “It’s hard to know which came first – the belief in the food being lucky, or the tradition of eating it because it was available, and then attaching meaning to it,” says food historian and author Andrew F. Smith.
More here.