The "true love" of the song refers to God.
The partridge in a pear tree was Jesus Christ.
Two Turtle Doves were the Old and New Testaments.
Three French Hens stood for Faith, Hope and love.
The four Colley Birds* were the four Gospels of Matthew, Mark, luke and John.
The five Golden Rings recalled the Torah or law, the first five books of the Old Testament.
The six Geese A-laying stood for the six days of creation.
Seven Swans A-swimming represented the seven gifts of the Holy Spirit: Prophecy, 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 disciples.
The twelve Drummers Drumming symbolized the twelve points of belief in The Apostle's Creed.
*Although most people say / sing "four calling birds", the actually birds are "four colley birds" (blackbirds).