Many reputable folkloric sources say that January 5, the Eve of Epiphany (which is Twelfth Day), is the night called Twelfth Night on which great revels used to take place all over Europe.
“The day before Epiphany is the twelfth day of Christmas, and is sometimes called Twelfth Night, an occasion for feasting in some cultures. In some cultures, the baking of a special King’s Cake is part of the festivities of Epiphany (a King’s Cake is part of the observance of Mardi Gras in French Catholic culture of the Southern USA).” Source
No less an authority than Encyclopedia.com’s article on the subject also claims the evening of January 5 as Twelfth Night. However, according to the great Sir James Frazer’s The Golden Bough:
“The last of the mystic twelve days is Epiphany or Twelfth Night, and it has been selected as a proper season for the expulsion of the powers of evil in various parts of Europe.”
So, to Frazer, Epiphany (January 6) is Twelfth Night. Moreover, in many places Twelfth Night is still celebrated on January 6 (see this site).
Until I’m shown an authority greater than Frazer, not to mention many eminent others, such as Waverley Fitzgerald from School of the Seasons (who has a very good article on the celebration), I will stick to January 6, Epiphany, as being both Twelfth Day and Twelfth Night, January 5 being Eve of Twelfth Day/Night.
Befana Fair, Italy
In many Italian communities, children are greeted today by a little old lady with a broom and a basket of gifts. Befana was the person who would not accompany the Three Wise Men, or Magi, on their trip to Bethlehem. Afterwards she could find neither the Magi nor the baby Jesus, and has suffered ever since.