In this chapter, Hezekiah orders for the tithe to resume.
The first verse in this chapter describes the fallout from Hezekiah's Passover. What we see is a religious wave, centered around temple worship, sweeping through not only Judah but also the northern tribes of Ephraim and Manasseh, and it destroys all of the symbols of idolatry as it passes through.
After this one verse, the Chronicler moves on to the central topic for this chapter, which is the resumption of the priestly ministry and the tithe.
These two concepts are closely related. The priests and Levites cannot afford to operate in a vocational ministry without the tithe, because that is how they get paid. The only other source of income the priests would have is from the sacrifices at the temple, but the Levites would have been excluded from performing offerings. Anyway, what we see in practice is that when the tithe is not collected, the Levites and priests usually go back to farming to provide for their families.
Hezekiah, however, wants to restart the temple worship system. He does this in three parts. The first part is commanding the priests and Levites to fulfill their ministry (v. 2). The second part is providing for the daily, weekly and monthly offerings, which are part of the Law stipulated in Numbers 28:1-15. However, while that passage orders Israel to make these regular offerings on behalf of the community as a whole, it does not provide a mechanism for funding the communal offerings (like who is supposed to pay for it). In v. 3, it appears that Hezekiah is willing to take that burden on himself, and since it refers to this as the "king's portion", it's possible that this was a normative practice throughout the kingdom period (i.e. that the king was always responsible for the regular temple sacrifices). If so, this practice is never specifically described anywhere and we can only infer it from context, such as here.
The third and final part is resuming the tithe (v. 4). Although the people were not previously bringing in the tithe, they respond to the king's command with remarkable enthusiasm, because very shortly after the command was given, we have these "heaps" that start to pile up, above and beyond the immediate needs of the Levites and priests. This motivates the second half of the chapter which is constructing store rooms to hold the excess food. I can't imagine they would store the animals or meat (unless it is preserved somehow), but they could easily be storing excess grain, oil and wine.
So what is the bigger picture of this chapter? When we take all these events as a whole, what we see is Hezekiah successfully restarting much of the temple system as it would have existed in the time of David and Solomon. After sanctifying the temple (chapter 29) and performing the first Passover (chapter 30), this chapter is Hezekiah restarting the temple sacrificial system and Levitical ministry. Many of these elements are derived from the Law of Moses, but many others are based on the Davidic system. In this chapter, two prominent examples of that are the divisions of the priests and the worship ministry (i.e. Levites as singers and musicians). Both of these examples are in v. 2. The priestly divisions and worship ministry are substantially unique to Chronicles, because they are not described in either the Pentateuch or in the Samuel/Kings narrative. From a literary point of view, this establishes a clear affinity between the narrative here and the earlier temple preparation narrative in 1 Chronicles. From a historical point of view, it shows that Hezekiah is looking to David for his model when reconstructing the temple worship system.
That is all concerning Hezekiah's role in this chapter. The other side is looking at how the people respond. In general, their response appears to be both enthusiastic and thorough. All the people who went to the Passover go around destroying altars, pillars and Asherah poles throughout both the northern and southern kingdoms. Later, the people are very energetic about giving the tithe, which is how you can tell they are really sincere, since nobody who is faking their religion would be energetic about giving away hard-earned cash.
Verses 20-21 conclude the chapter on a positive note, telling us that Hezekiah is such a great guy, and he's successful everywhere, and he sought the LORD with his whole heart, and everything is wonderful. This makes it all the more baffling when Hezekiah's son, Manasseh, is one of the worst kings that Judah ever has, and the people collectively go all the way back to Baal worship in just one generation. This is a question that I wrote about at length in my commentary on 2 Chron 29, so I won't repeat myself here, but I will say that passages like vv. 20-21 are a big part of what made it so hard for me to understand how the people returned to Baal worship. Or really this chapter as a whole, with the people acting so faithful to the LORD, so eager to destroy idols and give their tithes to the LORD: how do they turn to idolatry so quickly? For my speculation about the answer, read my earlier commentary.
Meanwhile, life for Hezekiah moves on. In the next chapter, Hezekiah faces one of the first big challenges in his reign, when Sennacherib and the Assyrians invade.