This passage's main ideas are that, first, God's plan is focused on Israel through the fulfillment of the promises, and second, that the Israelites are thus God's primary agents for bringing His plan to pass, particularly the house of David and its greatest scion, Jesus of Nazareth. God will sometimes use Gentiles, but he predominantly employs Israelites to drive affairs along in His plan.
These scriptures focus on the Branch as King, descending from David, making righteous judgments, ruling, and causing peace and security. Thus Revelation 19:16 calls Him, "KING OF KINGS AND LORD OF LORDS."
