Jesus is described as the Messiah or a King, or the savior of the Jews. Songs and stories emphasize that Jesus will save the Jews from all their sins, and he is the Almighty. Angels sing about his coming, and he will bring peace.
My song is "Little Drummer boy". This song is written in the view point of the visitors of Baby Jesus. It emphasizes how everyone who came brought gifts, the first verse says "Our finest gifts we bring… to lay before the King". In this song, Jesus is described as a "new born King".
In the Nativity Story, Mary and Joseph had to trust each other, and Joseph had to take extreme care for Mary and the unborn baby. He goes through troubles just to find Mary a place to give birth. Afterwards, the shepherds had to have faith and follow the star, same with the Persian astrologers. However, the Persian astrologers had to be careful of King Harod, because they knew if they went back to him, the King would kill Jesus immediately.
I think God sent Jesus down as a mortal baby to represent the humility of Jesus. Having a savior who lived the times, from a baby to adult, the people back then lived can help you realize that there was nothing superbly special like he couldn't die and whatnot.