Epiphany is a commemoration of the Magi visiting the Christ Child and giving gifts of gold, frankincense and myrrh. The first section of the novel Ben-Hur is a detailed account of how the wise men met in the desert before they followed the star to Bethlehem, if you are in a reading mood.
There is also a tradition of marking the entrance of your home with the year and the initials of the traditional names of the Magi - Caspar, Melchior ans Bathalzaar. "CMB" also stands for "Christus Mansionem Benedicat", Latin for "Christ, Bless this Home" It looks like this: 20 + C + M + B + 10.
Another tradition for this day is to have all the Christmas decorations taken down. That will take place over the next few days around here.