They came from afar. We also come from afar. We are by nature alienated from God our Creator. We must come from afar to seek Jesus.
Prophecy was fulfilled (Jeremiah 16:19). Amazingly, Jeremiah spoke of Gentiles coming to God and confessing they had inherited lies, worthless ness and unprofitable things from their fathers. These wise men are a fulfilment of Jeremiah’s prophecy.
A sign was given to the wise men - the star. Our sign is not a star but the Word of God (Bible) ministered to us by the Holy Spirit and giving us guidance.
We (unlike the wise men) seek not a child but a man. Jesus is the man
- the Mediator between God and men.
The wise men recognised that salvation is of the Jews. They asked “Where is he who has been born King of the Jews?” In God’s plan salvation came to the Jews first; then to the non-Jews.
The wise men recognised that Jesus was the Saviour. There was no Saviour for them in their homelands. They must come to Israel to meet the promised Messiah.
The wise men worshipped Jesus (not Mary).  Amazing! Adults falling down and worshipping a child! But not amazing when you consider who that child was.
“Jesus Lord at Thy birth” is wonderful theology. Jesus never gave up his deity. He was Lord even at birth.
The wise men gave the most precious of gifts. The most precious gift we can give is our lives (Romans 12:1)