What does Acts 13:34 mean?
Paul is explaining to a group of Jews and God-fearing Gentiles that God's saving work that sustained the Jews throughout their history is now manifested in the Savior He promised: Jesus. He has explained how the Jewish leaders in Jerusalem had Jesus killed despite His innocence, and that there are many witnesses who attest that God raised Jesus from the dead (Acts 13:27–31). Now Paul shows how Jesus' resurrection was prophesied in Hebrew Scripture.The quote is of part of Isaiah 55:3 from the Septuagint. In the broader passage, God is telling His people to come to Him, and He will provide what they need. They need to reject the world's values and rely on Him to provide what is good. Isaiah 55:3 reads, "Incline your ear, and come to me; hear, that your soul may live; and I will make with you an everlasting covenant, my steadfast, sure love for David." God's everlasting covenant with David promised David would have an heir—a Savior—who will sit on David's throne (2 Samuel 7; Acts 13:23). That covenant of blessings is manifested in Jesus, David's genetic, spiritual, and political heir. The "you" of Isaiah 55 is Isaiah's audience—locally the Jews destined to go into exile in Babylon, but ultimately everyone who looks toward God's Savior.
Acts 13:35 explains how the blessings of David can be everlasting and sure, or trustworthy: God's Holy One was raised from the dead and did not see corruption or decay, as promised in Psalm 16:10.