The song was composed by Catholics in England during the 16th Century. They were forbidden by law to practice their Catholic faith. The only legal church in england was the state church. To teach their children the basic doctrine, they used nonsense songs that would not raise the suspicions of the non-Catholics around them, but would remind the children of their faith.
On the first day of Christmas— the days of Christmas are counted from December 26th to January 6th, the traditional day for celebrating the coming of the wise men— also called the "Epiphany."
A partidge in a pear tree— is a reference to Jesus and the cross (a mother partidge will literally rist her life for her children. See John 10:14-15 and Matthew 23:37).
Two turtle doves— is a reference to the two testaments of the Bible (Old and New) and also could remind them of the sacrifice offered at Jesus dedication in the Temple when he was 12 (Leviticus 12:8, Luke 2:24).
Three french hens— is a reference to the three gifts given by the wise men (gold, frankincense, and myrrh; Matthew 2:10-11) or to 3 virtues of Christ; faith, hope and love (I Corinthians 13) or to the three persons of the Trinity (Father, Son and Holy Spirit).
Four calling birds— is a reference to the four Gospels— Matthew, Mark, Luke, and John.
Five golden rings— is a reference to the first five books of the Old Testament, the law of Moses, also called the Torah.
Six geese a-laying— is a reference to the six days of creation (Genesis 1:31-2:2). Remember, God rested on the 7th day.
Seven swans a-swimming— is a reference to the seven gifts of the Holy Spirit listed in Romans 12:6-8. Prophesy, service, teaching, encouragement, ocntribution, leadership, and mercy.
Eight maids a-milking— is a reference to the eight beatitudes listed in Matthew 5:3-10.
Nine ladies dancing— is a reference to the nine fruits of the Spirit described in Galations 5:22-23. Love, joy, peace, patience, kindnewss, goodness, faithfulness, gentleness, and self-control.
Ten Lords a-leaping— is a reference to the 10 Commandments (Exodus 20:3-17).
Eleven pipers piping— is a reference to the 11 original disciples wo did not forsake the faith (Acts 1:13) as Judas did in betraying Christ (John 17:12) and through whom the gospel was preached to the whole world (Matthew 28:19; Romans 10:18-21).
Twelve drummers drumming— is a reference to the twelve points of belief found in the Apostle's Creed (if you don't have a copy— check the back part of the hymnal next time you're in church).
Save this for use next Christmas time as a family Bible study— you'll be glad you did.