In this chapter, Asa continues to push Judah into worshiping the LORD.
I see two big themes in this chapter. The first theme is the contrast between seeking the LORD and worshiping idols, and the second theme is the contrast between having peace and being in conflict.
I think it's really interesting how this chapter is positioned directly after 2 Chronicles 14 because chapter 14 touches on the same themes, and in very similar ways. In chapter 14, it basically says that Asa removed the high places, sought the LORD and had peace. And then right after that, a large Cushite army comes up and attacks Jerusalem, shattering the peace, but only for a moment. Asa remains dedicated to God and God saves Judah and they defeat their enemies. Now in this chapter, a prophet comes out and tells Asa that without God, they would not have peace (v. 5), and when the people turn back to God then they had rest again (v. 15, 19).
Now, I think it's likely that the distress that Azariah is talking about in v. 3-6 is from before Asa became king. I also think it's clear that this prophecy and subsequent actions are from after Asa's victory over the Cushites, because the "spoil they had brought" in v. 11 is clearly referring to the plunder from 2 Chron 14:13-15. In light of that, we should interpret the prophecy as not referring to the deliverance from a specific conflict or distress, but as a continual promise of deliverance as long as Judah remains obedient to the covenant. The reason is that Judah just defeated their enemies and won a big victory. They do not even HAVE a specific conflict or distress that they need to be delivered from. Azariah's prophecy does not make any sense if you think it refers to some specific deliverance because Judah is already living in peace under Asa's reign.
Rather, Azariah is referring to Judah's older history, probably under some earlier king like Saul or maybe even the judges, and once again Azariah is directly associating Judah's peace or distress with the extent to which they seek and obey the LORD. This notion that blessings flow from obedience seems very typical for the covenantal promises in Deuteronomy, and I feel like this chapter is heavily influenced by the structure of the covenant in Deuteronomy. The part that's unique is how much of the focus is on peace versus distress. This chapter basically defines the blessing of God as when he "gave them rest" (v. 15).
I also find it peculiar that this chapter occurs right after the battle with the Cushites. When I first read this chapter I thought it was very strange that Judah is being promised peace immediately after they fought this enormous battle. Granted, they won the battle, but I can't help but wonder why they didn't get this promise before the big battle. If God is going to promise them peace, then why not stop the battle against the Cushites? It was something I also wondered about in light of the "rest" that the LORD gave to Judah in 2 Chron 14:6. I guess I wonder what this promise could mean if it didn't stop the big Cushite army from invading. It's not something I have a great answer for; I think God might have had a purpose for the Cushite invasion, to test Asa's resolve. Also, verse 19 says that there was no more war until the 35th year of Asa's reign. The timing of the battle is not dated, but we can guess from 2 Chron 14:1 that it was probably in the 10th year of his reign or around that time, which means that Asa lived for another 25 years without war. Even living in America I'm not sure that we have gone 25 years without fighting a war of some kind, so having 25 years of peace in the Mideast does seem like a fulfilled promise to me, considering what the LORD promised and what he asked for.
In any case, at least the intent of this chapter is clear. Asa removes the idols and high places as his act of obedience to the covenant, and God responds by granting his peace and rest as his blessing.
Both this chapter and the previous chapter are Asa's good years, when he responds to peace well (by seeking the LORD) and responds to conflict well also (by seeking the LORD). In the next chapter, we'll see what happens when Asa faces another conflict and responds to it poorly.