Jesus encountered the woman at the well when he was traveling through Samaria. Jews typically avoided Samaria because of enmity between the two groups of people, the Jews and the Samaritans.
The woman was astonished when Jesus revealed his knowledge of her life. She knew he must be a prophet in order to know such personal things about her. He spoke to her of "living water" and of water so satisfying she would never thirst again. He, of course, was speaking of spiritual matters.
She brought the villagers to him saying, "Is not this the Christ?". He was well received by the Samaritans and many of them believed on him.
Another event that occurred during this time was the healing of the nobleman's son. Even though the man wanted Jesus to go to Capernaum to heal his son, Jesus healed him by not going to the boy, but by only speaking the word.
When the man arrived at his home he learned his son had begun to recover at the very hour he was having the conversation with Jesus.