It means manifestation. This is when the Magi (The Three Wise Men) visited Christ after his birth.
Twelfth Night is actually the 5th January and all decorations and greenery should be removed from the house by the 6th January.
In times past sometimes a fruit cake was made for 12th Night. It had in it one dried Bean and one dried Pea. The Lad who had the dried Bean would be Lord for the day and the Lass who had the dried Pea would be his Lady for the day. They became "Lord and Lady of Misrule". This tradition went on till about the nineteenth century. It was normally the servants who played these people.
Victorian housewives use to vie with each other in a competition at Church Suppers by making an Epiphany Tart. This is actually a jam tart with intricate patterns made with pastry and the spaces filled in with jam. Sometimes the patterns were quite complicated to use lots of different jams.