We Three Kings
The verses to 'we three kings' are pretty wonderfully theological and wrap across most doctrines.
The gifts symbolize aspects of Jesus' ministry and purpose.
Born a King on Bethlehem's plain
Gold I bring to crown Him again
King forever, ceasing never
Over us all to rein
Gold is the gift to honor a King. It is offered in acknowledgement that Jesus is the King of His Kingdom. Prince of Peace, etc...
Frankincense to offer have I
Incense owns a Deity nigh
Pray'r and praising, all men raising
Worship Him, God most high
Frankincense is the incense burned in religious ceremonies. It is an offering to honor Jesus as God.
Myrrh is mine, its bitter perfume
Breathes of life of gathering gloom
Sorrowing, sighing, bleeding, dying
Sealed in the stone-cold tomb
Myrrh is the oil that is used to anoint a dead body before burial. It is offered as a prophecy of the way he would die.
Prefiguring the New Covenant
There may also be some symbolism in the three offerings in terms of Jesus as Priest, Prophet and King. Hebrews 9 says that inside the Ark of the Covenant was held a gold jar of Manna from Heaven, the Rod of Aaron which sprouted and the 10 Commandments.
These are also types for Jesus. Manna for Jesus as the Great Prophet, the rod for Jesus as the Eternal High Priest and the ten commandments for Jesus as the Lawgiver or King. And the Gifts reflect those items stored in the Ark. Gold for kingship, Frankincense for priesthood and Myrrh for prophecy.
They're offered to Jesus, but it is Mary, who accepts them as the Ark of the New Covenant.
Alas, I just read this in the Catholic Encyclopedia
The giving of gifts was in keeping with Oriental custom. The purpose of the gold is clear; the Child was poor. We do not know the purpose of the other gifts. The Magi probably meant no symbolism. The Fathers have found manifold and multiform symbolic meanings in the three gifts; it is not clear that any of these meanings are inspired
Apparently there is no inspired and obvious symbolism.