Paul contrasts Jesus’ physical descent from David and the spiritual declaration he was the Son of God. Although some detect a reference to Jesus’s human and divine nature in this verse, it is more likely Paul has in mind Jesus’s life prior to the resurrection and his life as a result of the resurrection (Kruse, Romans, 42).
As with the claim Jesus is the Son of God, Paul’s claim that Jesus was “descended from David according to the flesh” underscores his messianic claim. If Jesus is the Messiah and the Son of God, then he must be from the line of David. Both Matthew and Luke include genealogies in their gospels to connect Jesus to the line of David through Joseph. Based on 2 Samuel 7:14, Davidic origin of the messiah is found in several texts in the Hebrew Bible and the literature of the Second Temple period. For example:
Jeremiah 23:5 (ESV) “Behold, the days are coming, declares the Lord, when I will raise up for David a righteous Branch, and he shall reign as king and deal wisely, and shall execute justice and righteousness in the land.
Psalm 89:3–4 (ESV) You have said, “I have made a covenant with my chosen one; I have sworn to David my servant: 4 ‘I will establish your offspring forever, and build your throne for all generations.’”
4QFlor 1:10-14 [And] YHWH [de]clares to you that 2 Sam 7:12–14 «he will build you a house. I will raise up your seed after you and establish the throne of his kingdom 11 [for ev]er. I will be a father to him and he will be a son to me.» This (refers to the) «branch of David», who will arise with the Interpreter of the law who 12 [will rise up] in Zi[on in] the [l]ast days, as it is written: Amos 9:11 «I will raise up the hut of David which has fallen», This (refers to) «the hut of 13 David which has fall[en», w]hich he will raise up to save Israel. Martı́nez and Tigchelaar, The Dead Sea Scrolls Study Edition (Translations) (Leiden: Brill, 1997), 353.
4 Ezra 12:31-32 “And as for the lion that you saw rousing up out of the forest and roaring and speaking to the eagle and reproving him for his unrighteousness, and as for all his words that you have heard, 32 this is the Messiah whom the Most High has kept until the end of days, who will arise from the posterity of David, and will come and speak to them; he will denounce them for their ungodliness and for their wickedness, and will cast up before them their contemptuous dealings.
In each of these examples the messiah is related to David (the seed of David, a branch out of David, etc.) Psalm 89:3-4 and the fragmentary Dead Sea Scroll both allude to 2 Sam 7:14, a text which anticipates a son of David will rule in Jerusalem (Solomon), but also that a son of David will rule forever (Jesus). This future messiah in some way restores the broken line of David.
As Richard Longenecker points out, unlike the Synoptic Gospels, Paul does not usually connect the idea of Jesus as the messiah and his physical descent from David (Romans, 65). So why does he make the connection at the beginning of the book of Romans? Longenecker (and many others) suggest Paul is using an early Christian confessional statement in these verses. In order to connect with congregations he does not know, Paul alludes to a familiar confessional statement used in their worship.
Going a step beyond Longenecker, if this is a confessional statement, I would suggest this tells us something about the congregations in Rome. The language in the introduction is thoroughly Jewish and messianic. The gospel Paul preaches is about Jesus the Messiah, who is the son of God (a messianic title) and the fulfillment of the line of David (a messianic expectation). We know Jewish-Christian congregations in Rome were persecuted because they were rioting over Chrestus, likely an indication of intense debate within the synagogues over Jesus as the Christ.
Since Paul is the apostle to the Gentiles and has a well-deserved reputation for preaching a Law-free gospel to the Gentiles, it is important for Paul to begin his letter to messianic Jewish congregations with a clear affirmation that he believes Jesus is the Messiah and fulfills Jewish expectations about the Messiah.