The woman is an outsider on many levels.
1. She's a Samaritan. The Jews and the Samaritans have taken separate paths as a result of a spiritual rivalry, and have come to despise one another.
2. She's a woman. The disciples don't even notice her as they're walking away to get food. (Jesus apparently actually sent them in that direction as a test, to see if they would pay any attention to her.) When they return and find Him speaking with her -- speaking with a woman, it specifically says -- they're appalled.
3. She's had many husbands. Although we don't know the stories behind this, it seems feasible that at least one of her marriages ended in divorce, knocking her even further down the social status ladder.
4. She's living with her boyfriend. She could quite easily one day find herself stoned to death for this.
5. She's been rejected by the other women of the town. She's not someone a "nice person" should associate with.
So, she's clearly scratching her head, wondering for many reasons why Jesus is talking to her. She's adapted to being the invisible outsider -- coming to draw water at an unusual hour, for example, so that she won't run into the other women. But it must still hurt. Adapting to being an invisible outsider is a painful process: you have to give up, on many levels.
Jesus doesn't reproach her. He simply acknowledges her reality, and gives her hope. Amazingly, He even tells her directly who He is. Then, in contrast to what He said to His disciples when they figured out His identity, He doesn't add "and don't tell anyone." She tells the whole town about Jesus! Interestingly, they pay attention, and many people come to believe in Him.
As I said, there's enough material here for several books. But here's one aspect that strikes me, concerning, of all things, the Church and its outreach. What would have happened if the events in this story had been reversed? Suppose Jesus had seen the woman and had walked to the other side of the street to avoid her. Or, suppose He had spoken to her but had said something like, "You're a woman, you're sinful, and your people are doctrinally lost. I shouldn't even be talking to you. But here's the story of your life, and now here's how you can find eternal life." If the thought of hearing Jesus speak like that makes you squirm (it should), imagine His reaction to us, when we do and say similar things to spiritual and social outsiders. Suppose someone from an "unacceptable group" (possibly even a fellow believer) shows up at our church or at one of our homes. Will what they see and hear make them want to run and tell everyone about the loveliness of Jesus and the power of His saving grace, or will it make them just want to run?
There are a LOT of hurting people out there. Do we see them, or do we classify them as "not us" and dismiss them? People don't need to be cleaned up before they can meet Jesus, before He meets their gaze and offers them life. So why do they so often have to be cleaned up before we can see and meet them?