Why is David so significant?
David was the son of Jesse and the second anointed king of Israel. He is characterized as "a man after God's own heart" - see 1 Samuel 13:14 and Acts 13:22.
It is through David that the promises of God will be realized in Christ, David's descendant - see Matthew 1:1. The promises God made to David may be found in 2 Samuel 7:12-17 and compare Luke 1:31-35.
The story of David may be read beginning with 1 Samuel 16.