One of the main stories is the birth of Jesus. It details the events leading to his birth, like the visit of the Magi. Another is his Sermon on the Mount, where he taught important moral and spiritual lessons. Also, his miracles such as healing the sick are significant stories in the Book of Matthew.
In the Book of Matthew, there is the story of the Transfiguration. While it is known, it might be considered a bit less emphasized compared to some other stories. Jesus was transfigured on the mountain, and his appearance changed in front of his disciples. Also, the story of the ten virgins is there. It's a parable about being prepared for the coming of the Lord. And the story of the talents, which is about using one's gifts and resources wisely.
One important story is the Sermon on the Mount. It contains many of Jesus' teachings like the Beatitudes, which tell about blessedness in different situations. For example, 'Blessed are the meek, for they will inherit the earth.' This story gives moral and spiritual guidance.
One main teaching is about humility. Just as children are humble, we should be like that too. Another is about dealing with sin among people in a kind and private way.
We can understand the moral lessons by looking at the characters in the stories. Take the story of the prodigal son. The son who left home in a wasteful way and then returned. The father's forgiveness shows the power of mercy and unconditional love. We can learn from this to be more forgiving in our own lives.
In the Book of Matthew's account of the Christmas story, one of the main elements is the flight to Egypt. King Herod, fearing the new 'King of the Jews' (Jesus), ordered the massacre of all male infants in Bethlehem. But an angel warned Joseph in a dream, and he took Mary and Jesus to Egypt to escape. This part of the story shows the danger that Jesus was in from the start and also how God protected him.