from the Catholic News Agency:
The song, "The Twelve Days of Christmas" is an English Christmas carol. From 1558 until 1829, Roman Catholics in England were not permitted to practice their faith openly. Someone during that era wrote this carol as a catechism song for young Catholics. It has two levels of meaning: the surface meaning plus a hidden meaning known only to members of the Church. Each element in the carol has a code word for a religious reality which the children could remember. To fit the number scheme, when you reach number 9, representing the Fruits of the Holy Ghost, the originator combined 6 to make 3, taking the 6 fruits that were similar: the fruit in each parenthesis is the that was not named separately. There are actually Twelve Fruits of the Holy Ghost.
The "True Love" one hears in the song is not a smitten boy or girlfriend but Jesus Christ, because truly Love was born on Christmas Day. The partridge in the pear tree also represents Him because that bird is willing to sacrifice its life if necessary to protect its young by feigning injury to draw away predators.
And this from whychristmas.com:
The 12 Days of Christmas start on Christmas Day and last until the evening of the 5th January - also known as Twelfth Night. The 12 Days have been celebrated in Europe since before the middle ages and were a time of celebration.
The 12 Days each traditionally celebrate a feast day for a saint and/or have different celebrations:
Today is Christmas Day, the First Day of Christmas. On this day we celebrate the birth of Jesus.