What’s interesting are the changes we’ve made to the original story by "adding" to it over the centuries! Nowhere does it say that there were "three" Magi, but every kid and adult will insist there were three. Nowhere are they named, but over the centuries we have given them names (do you remember what they are?).
Nowhere does it detail from which countries they come, (only from the "east"), yet over time claims were made about that from other Old Testament parallels. Nowhere does it say that they are "kings," but we have always "assumed" this [but can you imagine three kings going off by themselves without their armies or guards?]. Some of the best known scholars believe the Magi were high-ranking advisors to pagan rulers.
As you will remember, Matthew has preceded this story with a "genealogy" to show that Jesus is descended from kings. This setting of "honour" is very important for Matthew, since he is talking about a young mother who was pregnant before she was married! Now three "Magi" pay the child great honour just by coming, and bringing very honourable gifts; they also do him homage. So it becomes a story about "honour" in a society where public honour was everything.
Once that is established, Matthew can now make his point. The glory of the Lord has been revealed to the world! He is recognised by the Gentiles, but not by his own people! There has now been an "epiphany" or manifestation of the Messiah, the divine Son of God to the entire world (pagan and Jew).
The "Messiah" or "Christ," words which mean "the anointed one," was conceived in Mary's womb by the power or "anointing" of the Holy Spirit, and this was manifested progressively, including the epiphany to the magi. The important underlying message is that the gift of salvation ("Jesus" means "God Saves") calls for a response of believing faith. The mission of Jesus was determined from the moment of his conception.
Just consider for a moment, what has been your response to his baptismal call for you to participate in his mission? What gifts do you bring to Jesus?