In this chapter, David divides the priests into 24 orders responsible for the temple ministry.
The basic purpose of this chapter is to set up a rotation for different priestly families to come and serve in the temple. This is quite similar to the previous chapter when David was organizing the Levites. Both chapters are part of David's preparations for the temple. The general progression of this book is that David has first defeated Israel's national enemies, establishing peace, then second he brought in great volumes of tribute and stone and wood to construct the temple. After collecting the materials for building the temple, David now seeks to prepare the administration of the temple by organizing the priests and Levites.
I think the biggest surprise to me in this chapter is that serving in the temple is actually only a small fraction of what the priests do with their time. Since there are 24 families who serve in the temple, that means each family will only spend 1/24th of their time in the temple service (this is slightly more than 4%). It doesn't say how long each period of service would be, but I think the most likely duration would be two weeks, because then 24 periods would be very close to one year in the Hebrew calendar.
Since so much of the biblical text is centered around the temple, worship and sacrifice ministries, I always imagined the priests spending their whole lives sacrificing animals and burning incense and stuff like that. I rarely ever thought of them as having an occupation outside of their official ministry at the temple or the tabernacle. And yet we can see that the priests spend only a tiny fraction of their time in the temple. What did the priests do when they weren't serving in the temple? We can figure out a couple possibilities based on the biblical text. Besides their responsibilities for monitoring skin diseases and mold, the priests were also selected to administrate Israel as officials and judges. 1 Chronicles 23:4 states that six thousand Levites would serve as officials and judges, but it's almost certain that the priests would do similarly and were most likely responsible for overseeing the Levites in whatever aspect the Levites administrated. The priests were "paid" through the tithe, so they did not have to do any farming or otherwise earn a living.
I don't have much more to say about this chapter. I think the majority of the names and families mentioned in this chapter are not meaningful elsewhere and the genealogical elements of this chapter are fairly unimportant to anyone who is not a scholar. I think we can understand this chapter as another phase of David's grandiose plan for building the temple, and that should mostly cover it.
In the next chapter, David's grandiose plans continue with the music ministry.