What is the context?
This verse is the meeting the magi have been seeking since they arrived in Jerusalem. Herod has asked them to report the child's location, while the star has led them to the house. They see Jesus with Mary, bow before Him, and present gold, frankincense, and myrrh. The next verse sends them home by another route after a warning in a dream.
The Greek verb translated worshiped is προσκυνέω, proskuneō (pros-koo-NEH-oh): to bow down or prostrate oneself before someone (Thayer's Greek Lexicon). Matthew first says the visitors fell down, then uses this verb for their bow before Jesus. They had come seeking the King of the Jews; the verb does not tell us everything they understood about Him.
Matthew describes a house and a child, without giving the child's precise age or the length of the family's stay in Bethlehem. The account names three gifts, not three visitors. Its immediate contrast is between the honor given here and Herod's murderous response in the following passage.
How is this passage commonly understood?
Christians commonly see the visitors as an early sign that Jesus' coming matters beyond Israel. The Catholic Catechism, paragraph 528, describes their adoration of Jesus and the welcome of the nations; Wesley's notes on Matthew 2:1–2 emphasize Gentile visitors paying homage to Israel's king. The Catholic teaching presents the visit within the revelation of Jesus as Son of God and Savior; Wesley's comment on the gesture stresses the honor shown to a monarch.
The gifts have also been read in more than one way. Irenaeus, Against Heresies 3.9.2, connects gold with kingship, frankincense with His being God, and myrrh with Jesus' death and burial. Wesley's note on 2:11 instead emphasizes valuable gifts suitable for a person of importance and suggests they provided help for the journey to Egypt. These are interpretations of the gifts' significance; Matthew names the gifts without explaining the visitors' intended meaning.
Where does this fit in God's plan?
The visitors' gifts and bowed posture recall Psalm 72:10–17, where distant rulers bring tribute and the nations receive blessing through the king. Isaiah 60:3–6 similarly pictures nations coming to the light with gold and frankincense. These are parallels that help explain the scene's place in the larger biblical story; they do not establish the visitors' titles or everything they personally understood.
Matthew's Gospel later makes the welcome of people from east and west explicit in Matthew 8:10–11, and ends with the mission to all nations in Matthew 28:18–20. This visit offers an early glimpse of honor coming to Israel's Messiah from beyond Israel.
What is our position?
What Does Worship Actually Mean? begins with the visitors' act of bowing down before the child they sought as King of the Jews. The scene does not tell us everything they understood about His identity.