What does 2 Samuel 13:38 mean?

Five years have passed since Amnon foolishly and selfishly raped his half-sister Tamar, believing himself to be lovesick for her. When David does nothing to hold his firstborn son accountable for that crime, Tamar's full-brother Absalom murders Amnon. Absalom flees to the home of his mother's father, the king of Geshur, to avoid being captured for his act of revenge.

Although Amnon is David's firstborn and Absalom is the thirdborn, there's no indication that Absalom kills Amnon to get a better position to succeed David as king. It's for the honor of Tamar and, by association, his own honor.

After three years, Joab, David's nephew and military commander, sees that David has sufficiently mourned for Amnon, and his heart is softening toward Absalom. Joab convinces a wise woman to tell David a real-sounding story that convinces him to invite Absalom to come home (2 Samuel 14:1–21).

Even so, David refuses to see him. He puts Absalom up in his own house for two years without reconciling. Absalom has to set Joab's fields on fire just to get David's attention. Finally, they meet again (2 Samuel 14:28–33).

For reasons only known to Absalom, he decides that reconciliation with his father isn't enough. He spends another four years winning the hearts of the people, giving them what they want when he can, and lamenting that he doesn't have enough power when he can't. Before David even knows what's happened, he's fleeing Jerusalem and his son is sitting on his throne (2 Samuel 15:1–17).