"The Twelve Days of Christmas" was written in England as one of the "catechism songs" to help young Catholics learn their faith.
The songs gifts are hidden meanings to the teachings of the faith. The "true love" mentioned in the song doesn't refer to an earthly suitor, it refers to God Himself. The "me" who receives the presents refers to every baptized person. The partridge in a pear tree is Jesus Christ, the Son of God.
The other symbols mean the following:
2 Turtle Doves = The Old and New Testaments
3 French Hens = Faith, Hope and Charity, the Theological Virtues
4 Calling Birds = the Four Gospels and/or the Four Evangelists
5 Golden Rings = The first Five Books of the Old Testament, the "Pentateuch", which gives the history of man's fall from grace.
6 Geese A-laying = the six days of creation
7 Swans A-swimming = the seven gifts of the Holy Spirit, the seven sacraments
8 Maids A-milking = the eight beatitudes
9 Ladies Dancing = the nine Fruits of the Holy Spirit
11 Pipers Piping = the eleven faithful apostles
12 Drummers Drumming = the twelve points of doctrine in the Apostle's Creed