The story
The magi followed a star from the east and brought gold, frankincense and myrrh. Epiphany means a showing: the point of the day is that the child was shown to strangers, from outside the people he was born into.
The twelve days between Christmas and today are the reason for Twelfth Night, and in much of the Spanish-speaking world the presents come now, from the three kings, rather than on the 25th.