“Praise be to the Lord, the God of Israel, because he has come to his people and redeemed them. He has raised up a horn of salvation for us in the house of his servant David (as he said through his holy prophets of long ago),
Luke 1:68-70 NIV
In direct lineage from King David through both His father (earthly, not biological) and His mother, Jesus of Nazareth, called the Christ and Messiah came into the world for one purpose - to seek and to save those who are lost (in sin).
When something is lost but found by someone else, to get the item restored to the original owner, it must be redeemed, or bought back. Man lost his way through sinning (breaking God's specific law) and was claimed by Satan, God's and our arch enemy. The price to redeem us to God was paid by God. He gave His only begotten Son, Jesus, as the price for our redemption.
The only substance of sufficient value to pay this price was the blood of Jesus. Because the life is in the blood His unique blood was priceless and therefore would cover the cost of redeeming all of mankind.
This was the fulfillment of God's promise to David and to Israel. But it was not just for them, it was also for the Gentiles (all the rest of the nations of the Earth). He promised and He delivered. Just believe on the Lord Jesus Christ and you will be saved.