What does 2 Samuel 7:13 mean?

The Lord is speaking to David about the son who will take the throne of Israel after him. Part of God's promise to establish David's kingdom forever is that He will be faithful to David's son. David already had many sons at the time of this revelation from God, but we know that son to be Solomon, born to David by Bathsheba.

God's promise to David is everything a God-honoring father could hope to learn about his son. The Lord promises that David's son will do the thing that David had wanted to do: He will build a permanent house, a temple, for God's name. Even more, the Lord will establish this son's kingdom forever.

At the Lord's direction, Solomon did, in fact, build the incredible temple which became the "house of God" in Jerusalem (1 Kings 5—6; 2 Chronicles 2—7). Not only was that a massive achievement, but Solomon's reign as king was marked by great prosperity and peace during his own lifetime.

But Solomon's throne doesn't last. When he dies, God punishes his idolatry and his son's foolishness by giving most of the nation to another man (1 Kings 11—12). About 330 years later, the Jews will be taken into captivity in Babylon. Except for a short time after the Maccabean Revolt, Israel won't be an independent nation again until 1948. And, even then, David's descendant doesn't reign on the throne—at least not as of this writing (Titus 2:13)!

Later, Ethan the Ezrahite will write a Psalm, imploring God to make his promise come true (Psalm 89). Neither David nor Ethan likely understood that God's peace and rest depend on Jesus, not David's fully-human sons.