Romans 1:3

regarding his Son, who as to his human nature was a descendant of David,

(v3, NIV)

This is talking about God's son. God sent his son into the world to become a man. This is who was chosen to redeem and save us. God didn't choose a man, he chose his son to become a man. This gospel of God is about God's son who he sent into the world to become a man to be the propitiation for our sins.

So what's so important about Jesus being a descendant of David? Well, the Jews were waiting for a savior. The Messiah who was spoken of and prophesied about in the Old Testament is who they were waiting for. He would come and great things were expected of him. One thing that was prophesied about him was the fact that he would be a descendant of David.

"The days are coming," declares the LORD,

"when I will raise up to David a righteous Branch,

a King who will reign wisely

and do what is just and right in the land.

(Jeremiah 23:5, NIV)

In that day the Root of Jesse will stand as a banner for the peoples; the nations will rally to him, and his place of rest will be glorious.

(Isaiah 11:10, NIV)

From the Old Testament we find these prophecies saying that Jesus is to be a descendant of David. These prophecies are fulfilled since Jesus is a descendant of David. Jesus is the fulfillment of prophecy; Jesus is the Messiah. The gospel is regarding Jesus, God's son.