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 their church. Each element in the carol has a code word for a religious reality which the children could remember.
One true love refers to God.
Two turtle doves were the Old and New Testaments.
Three French hens stood for Faith, Hope and Charity, the Theological Virtues.
The four calling birds were the Four Gospels and/or the Four Evangelists Matthew, Mark, Luke & John.
The five golden rings recalled the Torah or Law, first Five Books of the Old Testament, the "Pentateuch", which gives the history of man's fall from grace.
The six geese a-laying stood for the six days of creation.
Seven swans a-swimming represented the seven gifts of the Holy Spirit, the seven sacraments: Prophesy, Serving, Teaching, Exhortation, Contribution, Leadership, and Mercy.
The eight maids a-milking were the eight beatitudes.
Nine ladies dancing were the nine Fruits of the Holy Spirit: Love, Joy, Peace, Patience, Kindness, Goodness, Faithfulness, Gentleness, and Self Control.
The ten lords a-leaping were the Ten Commandments.
The eleven pipers piping stood for the eleven faithful apostles.
The twelve drummers drumming symbolized the twelve points of doctrine in the Apostle's Creed.