From the excellent article on Twelfth Night at Fisheaters.
The Eve of the Feast of the Epiphany is the twelfth day of Christmas, and tonight is known as"Twelfth Night" (or "Twelfthnight"). It begins the celebration of Christ's revealing His Divinity in three ways, which is formally celebrated tomorrow:
to the Magi who, guided by the great and mysterious Star of Bethlehem, came to visit Him when He was a Baby (Matthew 2:1-19)
through His Baptism by St. John, when "the Spirit of God descending as a dove" came upon Him and there was heard a voice from Heaven saying, "This is my beloved Son, in whom I am well pleased" (Matthew 3, Mark 1, Luke 3, John 1), and all Three Persons of the Most Holy Trinity were manifest (Note: the Baptism of Our Lord is also commemorated on the 13th of January)
through His first public miracle -- that of the wedding at Cana when Our Lord turned water into wine at the request of His Mother (John 2). Just as God's first miracle before the Egyptian pharaoh, through Moses, was turning the waters of the Nile into blood, Our Lord's first miracle was turning water into wine.
In many Catholic homes (especially Italian ones), it's not Christmas Day that is for giving presents to children, but the Feast of Epiphany, when the gifts are given in a way related to the Magi. So today will have a "feel" of Christmas Eve, and because of the Epiphany's association with the Magis' gift-giving, tomorrow is often referred to colloquially as the "Little Christmas."
It is today that the Three Kings should reach the creche (heretofore, they should be kept away from it) and that Baby Jesus should be adorned with signs of royalty, such as a crown, ermine, and gold or purple cloth. Set up golden candlesticks around the manger where He lies.
Along with the crowns, scepters, gold, and royal purple, peacocks are also a symbol for the day. They are more generally a symbol of immortality (and therefore a good symbol for Easter, too), but also a symbol of royalty and of the glory revealed by Christ today. The most profound symbols of all, though, are light as a symbol of theophany; wine in memory of the miracle at the wedding in Cana; water and the dove in memory of Christ's Baptism by St. John; the Three Kings, their gifts, and the Star of Bethlehem.
The Magi and Their Gifts
Typified in the Old Testament by the Queen of Saba (Sheba), who entered Jerusalem "with a great train, and riches, and camels that carried spices, and an immense quantity of gold, and precious stones" in order to ascertain King Solomon's greatness (III Kings 10), the three Magi entered Jerusalem bearing gold, frankincense, and myrrh for the newborn King. The Fathers see in their gifts omens of Christ's life:
the gold as a sign of His Kingship. The gifts of gold and frankincense were both prophesied by Isaias in the sixth chapter of his book.
the frankincense -- a gum resin (i.e., dried tree sap) from the Boswellia tree, native to Somalia and southern coastal Arabia -- as a sign of His Deity. Mixed with stacte, and onycha, and sweet galbanum, it was used by Moses to set before the tabernacle as an offering to God, and was considered so "holy to the Lord" that it was forbidden to use profanely (see Numbers 30).
the myrrh -- a brownish gum resin from the Commiphora abyssinica tree, native to eastern Africa and Arabia, and used in embalming -- as a sign of His death. Myrrh, along with cinnamon and cassius, was used by Moses to "anoint the tabernacle of the testimony, and the ark of the testament" (Numbers 30). It has analgesic properties, too, and was offered, mixed with wine, to Christ on the Cross, which He refused (Mark 15:23). Nicodemus brought myrrh to annoint Our Lord's Body after death (John 19:39).
The three Magi -- Caspar (a.k.a., Gaspar, Kaspar or Jaspar), Melchior, and Balthasar -- are seen as the "first fruits of the Gentiles" -- those outside of Israel who came to faith. They undoubtedly travelled from Persia (modern Iran, a distance of about a thousand miles from Bethlehem), and their ancestral origins are probably found in Persia, Babylon (modern Iraq), Arabia, India, and/or Ethiopia.
...How do we know there were three? We don't know that from Scripture, but tradition relates that were were three, and that there were three gifts mentioned supports this notion as well. Tradition says, too, that these three men were representative of the three ages of man and of the three "racial types" of man, the three families that descended from Noe's three sons (Sem, Cham, and Japheth). According to tradition, Caspar was the young, beardless, ruddy descendant of Ham who brought frankincense. Melchior was an old, white-haired, bearded descendant of Sem who brought gold. And Balthasar was a bearded black descendant of Japheth, in the prime of his life, who brought myrrh (see the works of the Venerable Bede).
Tradition also has it that the kings were baptized by St. Thomas, and they are considered Saints of the Church. Though their feasts aren't celebrated liturgically, the dates given for them in the martyrology are as follows: St. Caspar on 1 January; St. Melchior on 6 January; and St. Balthasar on 11 January.
The cathedral in Cologne, Germany contains the relics of the Magi, discovered in Persia and brought to Constantinople by St. Helena, transferred to Milan in the fifth century, and then to Cologne in 1163. Their trip to Cologne -- said to have taken place on three separate ships -- is the genesis of the carol "I Saw Three Ships", the lyrics of which were later amended to speak of the Holy Family rather than the Magi, and of their sailing to Bethlehem (a physical impossibility in real life) rather than to Cologne.
...The three stars that make up the belt of the constellation Orion are often called "The Three Kings" or "the Magi" in honor of the men who travelled so far to honor Our Lord. On a clear night, this constellation is easily seen in Winter's southern sky, so take your children outside to see a beautiful symbol, made of stars, of the men who followed the Star of Bethlehem. If you follow the line of the belt southward, you will see lovely bluish-white Sirius (the Dog Star), the brightest star in the night sky. It's as if "the Magi" are following the "Star of Bethlehem" forever...
Other Customs for the Day
After a nice candlelight feast (try adding some myrrh or frankincense fragrance oil to your candles tonight!), there is the tradition of drinking a medieval wassail called "Lamb's Wool," which is said to take its name from "La Mas Ubhal," which means "the day of the apple fruit" (and was pronounced like "lamasool"). "Three Kings Cake" is eaten in honor of the three kings, one slice being set aside "for God." Recipes for the latter vary from country to country, but they almost always include a trinket or dried bean hidden inside. The person who gets the slice with the trinket or dried bean is the King or Queen of the Day and gets to choose a consort (this is the French method). The King and Queen, once chosen, are honored, obeyed, treated and addressed as royalty. ...