When Jesus was in the area of Tyre and Sidon, a Gentile woman approached Jesus and asked him to heal her daughter who was possessed by a demon. After speaking with the woman, he praised her for her faith and told her that her daughter was healed. As explained in the Gospel of Matthew:
Jesus did not answer a word. So his disciples came to him and urged him, "Send her away, for she keeps crying out after us."
He answered, "I was sent only to the lost sheep of Israel."
The woman came and knelt before him. "Lord, help me!" she said.
He replied, "It is not right to take the children's bread and toss it to the dogs."
"Yes it is, Lord," she said. "Even the dogs eat the crumbs that fall from their master's table."
Then Jesus said to her, "Woman, you have great faith! Your request is granted." And her daughter was healed at that moment.
- Matthew 15:21-28, NIV translation.
Whereas Jesus died for the sins of all people, and while any person who has faith in Jesus as the Son of God (as explained in John 3:16-18) will have forgiveness and eternal salvation, Jesus' public ministry was directed primarily at the people of Israel.
The woman referred to Jesus as the "Son of David," perhaps because she realized he is the Messiah. The prophets of the Old Testament had previously revealed that the Messiah would be a descendant of King David, who lived about a thousand years before the time of Jesus. As explained in the Gospels of Matthew and Luke, Jesus was a descendant of King David.
Read more in the book Jesus the Miracle Worker: The 46 miracles of Jesus explained in chronological order (The Jesus Books) -- now available at amazon.