It is commonly believed that the white in the candy symbolizes the purity of the virgin birth of Christ and His holy, sinless nature. On a more secular note it can also refer to the purity of the...
Christmas. Red and White are the unofficial colors of Christmas. Notice that santa wears red and white as well. Aside from just trying to be relevant to Christmas they don't represent much anything...
One of the reasons thought to be was: A long while ago in churches, when kids cried, the priest would give them a white cane made of candy (Which represents a Sheppard's cane). Then a little bit...