The gifts were customary at the time, but also had profound symbolism.
When the Magi came to visit the newborn Christ Child, they did not come empty-handed. Saint Matthew narrates what happens when they first encounter the Holy Family.
[G]oing into the house they saw the child with Mary his mother, and they fell down and worshiped him. Then, opening their treasures, they offered him gifts, gold and frankincense and myrrh. (Matthew 2:11).
Surprisingly, this type of gift-giving was a standard way to honor a king or god in the ancient world. According to historians, “these same three items were apparently among the gifts, recorded in ancient inscriptions, that King Seleucus II Callinicus offered to the god Apollo at the temple in Miletus in 243 B.C.E.”
This means that the Magi were following “protocol,” by bringing these gifts to a child they believed would some day be a powerful king and who may also be a divine being.
Biblically speaking, Isaiah prophesied that these gifts would be given to the Messiah.
A multitude of camels shall cover you, the young camels of Mid′ian and Ephah; all those from Sheba shall come. They shall bring gold and frankincense, and shall proclaim the praise of the Lord. (Isaiah 60:6)
Traditionally these gifts have also been interpreted to have a specific symbolism. The gold represents Christ’s kingship; frankincense, a sweet-smelling resin used in worship, his priesthood; and myrrh, an ointment used in burial, foreshadows his death.
Myrrh is also closely related to the passion of Jesus, who was offered it as he hung upon the cross, “And they offered him wine mingled with myrrh; but he did not take it” (Mark 15:23).
This interpretation of the three gifts has been passed down since the first few centuries of Christianity and is held up as the primary meaning behind the gifts, even though the Magi themselves may not have fully understood the impact of their Christmas presents.