Chrysostom says that the water and blood are the source of the sacraments of Baptism and the Eucharist, which are central to the formation of the Church. Therefore, the Church, who is the Bride of Christ, was born from the side of Christ at this event.
St. Paul calls Jesus the "New Adam", the first of a new humanity. Chrysostom builds on this idea and compares the birth of the Church from Jesus' side to the creation of Eve from the side of the first Adam. What is important to Chrysostom is not that Eve was literally formed from one of Adam's ribs, but that the story is prophetic of the New Adam and his Bride.
Here is an excerpt from today's reading:
“There flowed from his side water and blood.” Beloved, do not pass over this mystery without thought; it has yet another hidden meaning, which I will explain to you. I said that water and blood symbolised baptism and the holy Eucharist. From these two sacraments the Church is born: from baptism, “the cleansing water that gives rebirth and renewal through the Holy Spirit,” and from the holy Eucharist. Since the symbols of baptism and the Eucharist flowed from his side, it was from his side that Christ fashioned the Church, as he had fashioned Eve from the side of Adam Moses gives a hint of this when he tells the story of the first man and makes him exclaim: “Bone from my bones and flesh from my flesh!” As God then took a rib from Adam’s side to fashion a woman, so Christ has given us blood and water from his side to fashion the Church. God took the rib when Adam was in a deep sleep, and in the same way Christ gave us the blood and the water after his own death.The text for this quote is taken from Universalis.com, and the picture is from Wikipedia.
Do you understand, then, how Christ has united his bride to himself and what food he gives us all to eat? By one and the same food we are both brought into being and nourished. As a woman nourishes her child with her own blood and milk, so does Christ unceasingly nourish with his own blood those to whom he himself has given life.