The following are the meanings of each gift sung within this carol:
The Partridge in a Pear Tree: This represents Jesus, as the partridge is a bird that will sacrifice its life to save its young.
Two Turtle Doves: These represent the Old and the New Testaments
Three French Hens: There are two theories on their meaning. The first being Faith, Hope, and Charity. The second being the three gifts of the Wise Men.
Four Calling Birds: These represent the four Evangelists: Matthew, Mark, Luke, and John.
Five Golden Rings: The rings represent the first five books of the Old Testament.
Six Geese a-laying: These represent the six days of creation, as described in Genesis.
Seven Swans a-swimming: These represent the seven gifts of the Holy Spirit: Wisdom, Understanding, Counsel, Strength, Knowledge, Piety, and Fear of the Lord.
Eight Maids a-milking: They represent the eight Beatitudes.
Nine Ladies Dancing: There are two theories to what these ladies represent. The first, the nine Choirs of Angels: Seraphim, Cherubim, Thrones, Dominions, Virtues, Powers, Principalities, Archangels, and regular Angels. The second, the nine Fruits of the Holy Spirit: Love, Joy, Peace, Kindness, Goodness, Patience, Gentleness, Faithfulness, and Self-Control.
Ten Lords a-leaping: The ten lords represent the Ten Commandments.
Eleven Pipers Piping: They represents the eleven faithful Apostles.
Twelve Drummers Drumming: This final gift represents the twelve points of belief in the Apostle's Creed.
Links:
http://www.new-life.net/chrtms18.htm
http://www.abcog.org/12days.htm
http://www.answers.org/holidays/twelvedb.html