My source is a current college student first experienced this custom from her father who was raised in Central Pennsylvania. At the beginning of every New Year, one must eat sauerkraut to bring in the New Year. She claims that her father was adamant about her eating the sauerkraut, suggesting strong symbolism behind the custom. She believes the folk custom to have come from the many Eastern Europeans living within Central Pennsylvania and their beliefs that sauerkraut was to be eaten on every New Year’s Day, though she does not for sure know why.
The eating of sauerkraut, in my opinion, is likely to bring in good luck and ward off the bad for the coming year, or it could be similar to the Korean tradition of eating a special type of soup that signifies the aging of one year when eaten on New Year’s Day. Eastern Europeans tend to be a superstitious people, however, and the warding off of bad luck seems to be the more realistic reason.