Saint Augustine provides a beautiful description of the episode of Christ and the Samaritan woman at the well. In this passage, he describes her as mystically representing the "Church not yet made righteous." You'll remember that Saint John highlights her position as an adulteress and as not pertaining to the Jewish people. Moreover, Christ initiates by asking her for a drink - which then leads to her desire for waters of life.
John's account profoundly highlights the ministry to the Samaritans as full members of the Church through baptism. Perhaps John was also recalling the time when he and Peter administered the sacrament of Confirmation to the first Samaritan believers (Acts 8:14). The incorporation of Samaria into the Church recalls the Messianic prophecy to reunite "all Israel."
Here's Saint Augustine:
A woman came. She is a symbol of the Church not yet maderighteous but about to be made righteous. Righteousness follows from the conversation. She came in ignorance, she found Christ, and he enters into conversation with her. Let us see what it is about, let us see why a Samaritan woman came to draw water. The Samaritans did not form part of the Jewish people: they were foreigners. The fact that she came from a foreign people is part of the symbolic meaning, for she is a symbol of the Church. The Church was to come fromthe Gentiles, of a different race from the Jews.
We must then recognize ourselves in her words and in her person, and with her give our own thanks to God. She was a symbol, not the reality; she foreshadowed the reality, and the reality came to be. She found faith in Christ, who was using her as a symbol to teach us what was to come. She came then to draw water. She had simply come to draw water, in the normal way of man or woman.
Jesus says to her: Give me water to drink. For his disciples had gone to the city to buy food. The Samaritan woman therefore says to him: How is it that you, though a Jew, ask me for water to drink, though I am a Samaritan woman? For Jews have nothing to do with Samaritans.
The Samaritans were foreigners; Jews never used their utensils. The woman was carrying a pail for drawing water. She was astonished that a Jew should ask her for a drink of water, a thing that Jews would not do. But the one who was asking for a drink of water was thirsting for her faith.
Listen now and learn who it is that asks for a drink. Jesus answered her and said: If you knew the gift of God, and who it is that is saying to you, “Give me a drink,” perhaps you might have asked him and he would have given you living water.
He asks for a drink, and he promises a drink. He is in need, as one hoping to receive, yet he is rich, as one about to satisfy the thirst of others. He says: If you knew the gift of God. The gift of God is the Holy Spirit. But he is still using veiled language as he speaks to the woman and gradually enters into her heart. Or is he already teaching her? What could be more gentle and kind than the encouragement he gives? If you knew the gift of God, and who it is that is saying to you, “Give me a drink,” perhaps you might ask and he would give you living water.
What is this water that he will give if not the water spoken of in Scripture: With you is the fountain of life? How can those feel thirst who will drink deeply from the abundance in your house?
He was promising the Holy Spirit in satisfying abundance. She did not yet understand. In her failure to grasp his meaning, what was her reply? The woman says to him, Master, give me this drink, so that I may feel no thirst or come here to draw water. Her need forced her to this labor, her weakness shrank from it. If only she could hear those words: Come to me, all who labor and are burdened, and I will refresh you. Jesus was saying this to her, so that her labors might be at an end; but she was not yet able to understand.
Saint Augustine, Tract. 15, 10-12. 16-17: CCL 36, 154-156.