From the Friars: Holy Smoke
Some people are incensed by incense due to it sometimes causing coughing or difficulty in breathing. I have that problem myself with certain types of incense. But it has had a significant role in the worship of God since the time of Moses. In the desert Tabernacle and later in Solomon’s temple there was a gold altar of incense directly in front of the veil that led to the Holy of Holies, the most sacred place where the Arc of the Covenant was kept and God dwelt in a unique way. On the Day of Atonement, the High Priest burned incense in front of the Ark so that the smoke would protect him from death due to being in God’s presence.
The frankincense given to Jesus at His birth was a recognition of His Divinity. Many early Christians won the crown of martyrdom for refusing to burn incense to the false gods of Rome or to the emperor. St. Polycarp for example, was tortured and burned to death for refusing to place just a pinch of incense on the coals burning before the statue of Cesar.
Sacred Scripture and tradition teach us about the various meanings that incense has in the Liturgy. The emanating smoke symbolizes our prayers rising up to God, and the fragrant odor that these supplications are from a pure heart and a clean conscience, pleasing and acceptable to the Most High. St. Thomas Aquinas teaches that incense makes visible the reverence due to the Most Blessed Sacrament, and shows the effect of the grace of Our Lord. The sacrifice of Jesus is the source of grace, and it spreads like smoke and the pleasing odor by us to every place.

Incense at a Catholic mass, by JoeJ10 – CC BY-SA 4.0, Link
The earthly liturgy is a foretaste of the heavenly liturgy. (SC no. 8) The worship of the angels and saints, in Christ our Head and High Priest, is actually made present. St. Ambrose teaches that incense is a visible sign of the presence of the Holy Angels, and they bear our prayers to the heavenly throne.
Let us see, and smell, the incense of the sacred liturgy with eyes and noses of faith. And may this Lent help us to become ready to enter our Heavenly Home.
Amen.
–Fr. Peter