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:
21 Jesus went out from there and withdrew into the region of Tyre and Sidon. 22 Behold, a Canaanite woman came out from those borders and cried, saying, “Have mercy on me, Lord, you son of David! My daughter is severely possessed by a demon!”
23 But he answered her not a word.
His disciples came and begged him, saying, “Send her away; for she cries after us.”
24 But he answered, “I wasn’t sent to anyone but the lost sheep of the house of Israel.”
25 But she came and worshiped him, saying, “Lord, help me.”
26 But he answered, “It is not appropriate to take the children’s bread and throw it to the dogs.”
27 But she said, “Yes, Lord, but even the dogs eat the crumbs which fall from their masters’ table.”
28 Then Jesus answered her, “Woman, great is your faith! Be it done to you even as you desire.” And her daughter was healed from that hour. (Matthew 15:21-28, WEB)
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' initially focused his public ministry on the people of Israel before expanding it to all people.
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 is a descendant of King David.
Read more in the book Jesus the Miracle Worker: The 50 miracles of Jesus explained in chronological order (The Jesus Series) -- now available at amazon.
Next: Miracles of Jesus: Healing a deaf man with a speech impediment (Mark 7:31-37)