In this long, long chapter, the author recounts the dedication offerings for the "altar."
There are two altars related to the tabernacle, the bronze altar of burnt offerings that lies outside the tent and the golden altar of incense that is within the holy place. The "altar" referred to in this chapter is almost certainly the bronze altar, because that is the larger and more prominent altar. The altar of incense is relatively minor in comparison.
I thought we had already dedicated the altar back in Lev 8, and that is correct. The first part of this chapter, verse 1, is essentially recapitulating what Moses did in Lev 8. However, the dedication offerings of the twelve tribes were not discussed in Leviticus, so I believe v. 1 of this chapter is simply placed here to set the context for the rest of this chapter. After the dedication offerings, in v. 89 at the end of this chapter, the LORD speaks to Moses and gives him instructions which are related to us in chapter 8, and possibly into chapter 9, though it's not clear if that's a separate event or part of this same narrative.
The offerings involve two portions, the carts with oxen and the daily offerings from each tribe which involve all of the major Levitical sacrifices: burnt offerings, a sin offering and peace offerings. A grain offering is not specifically mentioned, but grain would be typically offered in conjunction with the other offering types.
The carts and oxen are given to the two Levitical families that are allowed to use them with twice the oxen given to the Merarites, probably because they carry the poles, bars and silver bases which weigh more than the curtains and skins. The Gershonites are responsible for the curtains and skins and for that they are given two carts. Carts and oxen are probably very expensive given how few are offered for each tribe.
Now to address some details of this chapter, the order of tribes when giving offerings is precisely identical to the order of tribes in the census and the order of the camp in Num 1 and 2 respectively. The list of leaders for each tribe in this chapter is identical to the leaders in Num 1 and 2. Also, each paragraph for a given tribe is precisely identical to the rest, with the exception of the name of the tribe, its leader and the day the offering is given. Even though Judah is again given the honored first position, I think the overall effect is to emphasize the equality of the tribes because they each give the same gift.
It is funny that the author wrote out the full list of details for each offering, including the weight of the pans and bowls and everything. This is one of the longest chapters in the bible and yet it really doesn't include that much unique content because so much of it is repeated. The OT is funny, because it includes excessive, overbearing detail in some parts and it is inscrutably terse in other parts. Clearly this is one of the chapters with excessive, overbearing detail, which leaves us wondering why it was important to the author. I mean, he had to write all this stuff out by hand. I've spent some time writing things out by hand, and after about 50 pages it starts getting brutally tedious.
So I do believe there was something important about this to the author, but like so many things from the OT, I think the importance is lost on us. It makes me wonder, though.
Another minor point I'll bring up here is the imbalance between the burnt, sin and peace offerings. Numerically, the smallest is the sin offering which involves a single animal per tribe. Next is the burnt offering with 36 animals total, or 3 per tribe, and vast outnumbering either of these is the peace offering with a total of 204 animals. This highlights the distinct nature of the different offerings.
To wit, with a sin offering, the idea is that a single offering is enough. The purpose is to atone for sin, but for whatever reason, you only need kill a single animal to achieve this. In a similar vein are the Yom Kippur offerings, which involves a few sacrifices, but the core offering is a single male goat for a sin offering, whose blood is sprinkled on the atonement piece above the ark of the covenant.
Burnt offerings do not have a single distinct purpose, so it's hard to categorize them. In some cases the Israelites offer many burnt offerings, but in this case the number is relatively contained. The peace offering is the sacrifice most associated with feasting, and so in celebrations we will see e.g. hundreds or even thousands of peace offerings at a single time (for instance, 1 Kings 8:63 involves the peace offering of 142,000 animals). This is because the peace offering does not have a specific function like the sin offering, but can be offering simply as part of a celebration or feast. The size of the offering is usually dictated by the wealth of the offerer more than anything else.
The last thing I want to point out is that Moses hears a voice speaking from above the atonement piece on the ark of the covenant, which shows it to be kind of like a divine throne for the LORD, seated between the two cherubim. I talked about this before when discussing the construction of the ark in Ex 25, but verse 89 confirms this idea.