Why was the Miracle at the Wedding at Cana included in the Gospel of John?

¹ On the third day there was a wedding in Cana of Galilee, and the mother of Jesus was there. ²Jesus and his disciples had also been invited to the wedding. ³When the wine gave out, the mother of Jesus said to him, "They have no wine." ⁴And Jesus said to her, "Woman, what concern is that to you and to me? My hour has not yet come." ⁵His mother said to the servants, "Do whatever he tells you." ⁶Now standing there were six stone water jars for the Jewish rites of purification, each holding twenty or thirty gallons. ⁷Jesus said to them, "Fill the jars with water." And they filled them up to the brim. ⁸He said to them, "Now draw some out, and take it to the chief steward." So they took it. ⁹When the steward tasted the water that had become wine, and did not know where it came from (though the servants who had drawn the water knew), the steward called the bridegroom ¹⁰and said to him, "Everyone serves the good wine first, and then the inferior wine after the guests have become drunk. But you have kept the good wine until now." ¹¹Jesus did this, the first of his signs, in Cana of Galilee, and revealed his glory; and his disciples believed in him. -John 2:1-11

This story is interesting but why was it included? Was it because it was the first miracle that Jesus did?

When the author says that this was "the first of his signs ... and revealed his glory" he is implying that miracle showed Jesus' nature, who he was and what he came to do. For instance, the dialogue between the steward and the bridegroom has a much deeper message than what you read on the surface. If we only take the surface meaning that we can conclude that Jesus not only has the power to make water into wine, but he can make very good wine. Doesn't seem like a very important point. That is because the author is trying to show something else.

This dialogue between the steward and bridegroom is prophetic. Jesus is the good wine that was saved until the end. Many, many prophets were sent including great ones such as Moses, Elijah, and Daniel, but the reader is meant to pick up on the fact that Jesus is the greatest of them all. He was saved for last - "the best wine last". This is the wisdom and kindness of God to send his greatest prophet last.