In this chapter, Absalom takes Jerusalem and sleeps with his father's concubines, in fulfillment of the prophecy of Nathan.
This chapter begins with an interesting little story about Ziba and David. If my readers may recall, Ziba was a former servant of Saul who, in 2 Samuel 9, David assigned to administrate Saul's former estate on behalf of Saul's crippled son and heir Mephibosheth. David also commanded Mephibosheth to reside in Jerusalem rather than his tribal homeland of Benjamin, so we can reasonably understand that both Ziba and Mephibosheth are in close proximity to David at this time.
This part of the story is continuing with the "parade of various groups and officials who meet with David on his way out". Ziba says that Mephibosheth remained in town because he expected to be given the kingdom back, and David in turn rewards Ziba by promising to give him the entirety of Saul's estate when David has taken back the kingdom.
I think the last part of this exchange is the most peculiar. First of all, let us note that we only have Ziba's word at this point. Ziba is telling us that Mephibosheth is disloyal to David (which is not in itself unlikely given David's history with his father Saul), but keep in mind that Mephibosheth literally cannot walk out to meet David without help. If Ziba left him behind, Mephibosheth could do nothing about it. So just from that basis alone, we have reason to distrust Ziba's words.
Secondly, let us note how strange it would be for Mephibosheth to expect himself to get the kingdom when Absalom is himself coming to take it. I can't imagine any possible reason why Absalom would be inclined to just hand the kingdom over to Mephibosheth, and at this point it seems equally unlikely that the men of Israel would turn it over to a politically insignificant cripple. I hate to say this, but in Israel's society at the time people with physical infirmities were looked down upon. Like many cultures, it valued power and strength and regarded weakness and poverty as a curse from God. So if Mephibosheth really thought this, then he was badly mistaken; but it seems more probable to me that Ziba is simply lying because he was hoping to get a reward, and that's exactly what he gets.
After Ziba, the parade ends with Shimei, a relative of Saul (and perhaps meant to be contrasted with Ziba, who also served in Saul's house). Shimei curses David as a "man of bloodshed", which is ironic considering the history of Saul and David's repeated mercy towards him. David sheds blood in his subsequent war against Abner and Ish-Bosheth, who both died contrary to David's wishes. David certainly was guilty of bloodshed in the death of Uriah, which is the most direct cause for his present crisis. So I think it's an interesting question whether or not David is a man of bloodshed.
Abishai, for his part, proves himself to be a man of bloodshed by asking permission to kill Shimei, and David (in many ways) proves himself innocent by rebuking Abishai and accepting not only the humiliation of being driven out of his home, but the disgrace of being cursed on his way out. As in many other situations, David proves his worth by placing his hope and expectation in the LORD, that "the LORD will look on my affliction and return good to me instead of his cursing." David has definitely made mistakes, but it looks like he has developed a lot of humility and he accepts both curses and blessings, in hope that the LORD will do good for him and secure his life.
The chapter concludes when Absalom enters Jerusalem. He enters alongside Ahithophel (signifying Ahithophel's prominence in the revolt), and Hushai greets him. Absalom is skeptical, but is eventually deceived and accepts Hushai as one of his counselors. He then sleeps with David's concubines publicly, which fulfills the curse from Nathan that David received back in 2 Samuel 12. He is told to do this so that he can deliberately alienate himself from David. Besides the obvious reason (he is sleeping with some of David's wives), this is also an act that directly challenges David's kingship. We've seen this a couple times, but sleeping with a man's wife or concubine is (in Israel's culture) equivalent to saying, "I have inherited this man's wives along with his estate." You are claiming inheritance over his possessions, and not like "in the future I will inherit these things", but it's like you are taking their possessions and wives in the present tense, as if that man were already dead. Reuben did this when he slept with one of Jacob's concubines (Gen 35:22), and Ish-Bosheth accused Abner of doing it (2 Samuel 3:7). Now Absalom does it to challenge David publicly, in order to strengthen the hearts of the men who sided with him against David.
Rashi* has an interesting suggestion why this act would strengthen Absalom's rebellion. Remember how Absalom murdered Amnon, was driven into exile, but then reconciled to David? Amnon himself raped his half-sister and David did nothing. So over multiple situations, David has shown himself sensitive towards his children, even when they do horrible things. So Rashi suggests that when Absalom sees David, or if David starts to threaten Absalom, Absalom may have a "change of heart" and return to David. David has shown that he is likely to forgive his children, and that would leave Absalom's many supporters likely to die in subsequent crackdowns. Therefore by intentionally aggravating David, all those who wish to support Absalom can be more confident that Absalom will not betray them in turn.
Rashi puts it more succinctly: "For now they [lit., their hands] are lax to support you for they say in their hearts: the son will have a change of heart when [he is] near his father and we [alone] will remain despised by David." But I think the more critical factor here is how David has shown multiple times that he is likely to accept his son if his son returns to him, leaving all of Absalom's supporters "despised by David".
So all things considered, I think sleeping with David's concubines is actually a very astute political maneuver, and at the same time it fulfills Nathan's curse.
*Rashi is an excellent 11th century CE Jewish commentator who wrote a full commentary on the OT based on the existing Jewish Talmud (earlier commentaries from the 2nd through 5th centuries CE). You can find Rashi's commentary online at www.chabad.org which is a great resource in general for studying the Torah (i.e. the Old Testament).