We all know Christmas Day is the 25th December and many will know about Epiphany on 6th January. Also we are familiar with the song The Twelve Days of Christmas. These three things and their relationship causes the confusion over Twelfth Night.
There used to be a festival called Christmastide which lasted twelve days and was followed by Epiphany, which celebrates the Wise Men visiting the baby Jesus. The first day of Christmas is Christmas Day and so the twelfth day is 5th January. So Twelfth Night is 5th January.
Somehow Twelfth Night and Epiphany have been conflated to be the same thing, but they are not.