In this chapter, David defeats his enemies and establishes peace throughout Israel.
The contents of this chapter is substantially copied from 2 Samuel 8, which I have already written about here. The only variation I can find is that Chronicles omits part of 2 Samuel 8:2 when it says that David killed two thirds of the Moabites, even though the chapter contains references to the many other people that David's armies killed (v. 4, 5, 12) so I'm not sure why the Chronicler thought this one particular massacre was inappropriate.
There are two, or perhaps three, reasons why this material is relevant in Chronicles, again with our thoughts focused on the promises for Israel and the future temple.
First, the wars established the necessary peace for building the temple. There is a very clear distinction between the lives of David and Solomon. David made his reputation at first for slaying Goliath and becoming a commander over Saul's army. He spent much of his life running away from Saul, hiding in the desert, and then later fighting several wars against the Philistines, a civil war against Saul's heir, and internal rebellions led by his own sons. Solomon, on the other hand, lived in a peaceful and prosperous time and he spent much of his time building the nation. Even his name means "peace". This is not accidental; the peace and prosperity that existed in Solomon's time, and the vast army of conscripted workers (1 Kings 5:13-16), would not have been possible without David establishing military dominion over the surrounding nations. If David had not fought these wars, it would have been left to Solomon's generation to fight these battles and then the temple would have been delayed.
Second, the wars provided the gold and tribute David needed to save up in preparation for the temple. We see this in the many kinds of tribute that David collects from the Moabites (v. 2), the Arameans (v. 6-8), the gifts from Hamath (v. 10) and plunder from many other nations (v. 11). We see in v. 11 that David is not gathering this wealth for himself; he is dedicating it to the LORD. If you remember from 1 Kings 6, the temple is covered in gold all around the holy place and many of the utensils and the small altars are made out of gold. Where does all this gold come from, though? A lot of the gold and silver that we see adorning the temple is being looted right now from these hostile nations. Without this wealth, Solomon could not have built the temple with the same opulence that we later observe.
Third, it shows God's blessing upon David. I think this is the weakest point because there are many other places where the Chronicler shows God's blessing upon David, so this chapter is not necessary to establish that point.
Also, something that may be confusing is verses 9-10 when it says that a particular king Tou (or Toi) sent messengers to bear David gifts when he defeated the kingdom of Zobah. We don't really know anything about the situation beyond what is written here, but we can infer from the text that Zobah and Hamath were at war with each other, so the king of Hamath was pleased when he learned that David defeated his enemy. We don't know for sure, but that is by far the most likely explanation.
Overall, I think we should see this as a necessary step towards building the temple. In the next chapter, the battles against David's enemies continue.