In this chapter, David brings the ark of the covenant back to Jerusalem.
The content for this chapter is derived from 2 Samuel 6:12-16, but with significant expansion. The story in Samuel tells us the same basic facts, that after the LORD broke out against Uzzah and David left the ark in the home of Obed-Edom that he came to bring it back up to Jerusalem. It also implies to us in 2 Samuel 6:13 that on the second trip, it was carried up by the Levites according to the statutes. But Chronicles makes significant elaboration on this point, with over half this chapter dedicated to telling us the names of the Levites who came to carry the ark, David's specific instructions that the Levites are supposed to carry the ark, and the associated worship ministry that David instituted to go along with the ark.
I think this is consistent with the previous chapter, in verse 12 when it says that David's men burned the idols with fire. In this chapter, I think the Chronicler is trying to be a lot more specific about exactly what David does to dissuade the LORD's wrath. We could have known the commandments by reading the book of Numbers, but the Chronicler wants to be very specific in verse 15 and tells us that Moses commanded the ark to be carried on the Levites shoulders. This is why the LORD "broke out" against Uzzah and by implication, against Israel as a whole (v. 13). Now that the people are following God's commandments, the LORD "helps" the Levites (v. 26).
There is a notable emphasis on the role of the priests and Levites all throughout this chapter. The Chronicler specifically names all three tribes of the Levites (Gershon, Merari, Kohath) as well as three additional families that are not mentioned (or at least not prominent) in the book of Moses. None of this material is present in Samuel. From what I can tell, I think at least some of these families were involved with the Levitical worship ministry under David. This ministry is mostly ignored in Samuel but it forms a major part of the Chronicles narrative. It's possible this is because it is an important ministry during the post-exilic reconstruction when Chronicles was written. We can't know for sure, but it seems plausible at least.
David associates himself with the Levites by wearing a linen ephod, the traditional dress of the priests and Levites. This is part of the Samuel narrative as well, but I think it takes on added meaning in this chapter which focuses so much on the Levites. It shows that David is a king who supports the Levites and it's as if David wishes he could be a priest himself.
Verse 11 is a bit awkward. In context, both Abiathar and Zadok are regarded as "the priest", i.e. co-high priests. The Law of Moses does not have any provisions for two high priests, there is only supposed to be one. We know from elsewhere that eventually Abiathar will fall into disrepute as he sides with Adonijah in rebellion against Solomon and the priesthood is taken away from him. From that point, Zadok is the sole high priest and it seems like many parts of Chronicles are designed to validate Zadok's position as high priest. So the reference here to both Abiathar and Zadok must be uncomfortable for the Chronicler who sometimes appears to be trying to eliminate Abiathar from the historical record.
The triumphal festival around the ark seems to echo the festival in chapter 12 when David was made king. In that chapter, the people have a grand celebration, eating and drinking for three days to celebrate the newly crowned king David. In this chapter, they host an even greater celebration to celebrate the return of the ark of the covenant, bringing back God's presence to Jerusalem. God is the "great king" over Israel, so it's only appropriate that they would celebrate his return.
Verse 29 is interesting because it references the story of David's ascension over the house of Saul through his political marriage to Michal. The rest of the story is omitted, both the conflict between David and Saul as well as the situation that led to David's marriage with Michal. The text presumes that the reader knows this story. Chronicles also omits the exchange between David and Michal that is recorded in 2 Samuel 6:20-23 which mentions the conflict between David and Saul.
Rather than dwell on these unpleasantries, in the next chapter Chronicles swiftly moves on to describe the new tent for the ark and the Levites' song of praise to God.