This is a question that came up over the Christmas period, and I thought it would be good to answer it a little bit after Christmas, rather than try to remember it in time for next Christmas.
Frankincense and Myrrh are both resins, the hardened sap, of plants, which are used for making perfumes, and used for incense in religious rituals throughout the ancient middle east. Because of their mention as gifts to Jesus, they have become incense used in the Roman Catholic tradition. If you ever go to a big formal service, or mass, in a Roman Catholic Cathedral, you’ll see them waving incense around, and it might by Frankincense or Myrrh.
Frankincense was used in the Jewish Temple as incense, and myrrh was used as part of the embalming process by the ancient Egyptians.
There is no record of why these were chosen as gifts, but they were very expensive (as was gold, the other recorded gift) and not uncommon as gifts for important people.
It is possible that this was part of their trade cargo, part of the way they financed their trip to Jerusalem to find the new-born king.
There are traditional interpretations which give symbolic meanings of kingship, divinity and priesthood, or variations of that, but that seems a little bit much for what were fairly common gifts among the very wealth and important.
As such, these gifts demonstrate a desire to honour Jesus by giving him what is appropriate to someone of his station – a question we should ask ourselves about what we give to Jesus from our lives.