In this chapter, we are told what animals may be eaten.
Before commenting on the details, I would like to point out that this chapter divides the animals into ~5 groups: land animals, fish, birds, winged insects and swarming things. This is highly consistent with the subdivision of life that we found in Genesis 1, suggesting that it is a canonical classification to the ancient Israelites. I made a big deal out of this before, so it's encouraging to find more evidence that suggests that these ~5 groups are how the Israelites thought about other types of life.
Second, note that the precise identification of the animals in this chapter is generally quite sketchy. A lot of the words here describing animals are infrequently used, highly allusive, or simply imprecise in meaning. Some, especially the more common animals, are well defined, but these lists typically include both common and rare animals. For instance, the Hebrew word "yanshuph" in v. 17 is used to possibly describe a "great owl", yet according to Strong, the root word is "apparently from" malak, which means angel. Various translations differ in their treatment of this animal, partially because it's hard to figure out what bird is intended and partially because the ancient Hebrews did not have the same kind of taxonomy we do today. It's possible many distinct species (by today's metric) are grouped together into a single Hebrew term.
There are many such lists of animals or insects in the OT, and they are all generally hard to identify with precision, which isn't a big problem for us because it doesn't really matter, and for the ancient Israelites they would have known what these words meant, so it wouldn't have been a problem for them either. I just mention it because various bible translations typically have a lot of variance in their translations of these proper nouns, and now you know why.
Having said all that, the laws in this chapter seem generally pretty arbitrary. For land mammals and fish there are specific rules that govern what can be eaten, and for birds there is just a list of unclean birds (with the presumption that everything else is clean). And so on, I won't repeat the laws here. I've heard a couple different explanations for why these particular animals are prohibited (not from reputable sources, just from various realms of the internet). First, I have heard that it's because the prohibited animals would have caused problems if they were consumed while in the desert, because they rot fast or carry diseases or whatever. Second, I have heard it's because of certain double entendres in the prohibition against eating mammals, that the cloven hoof denotes the principle of separation from the world, while chewing the cud references meditation. Obviously this doesn't explain the other prohibited animals.
Neither of these explanations are particularly convincing to me without harder evidence, and to be fair, I've never really studied the matter. I think the general concept of "rules for desert living" is pretty reasonable, considering some of the other laws really do concern camp maintenance and disease prevention, yet they are constructed as ceremonial laws. I think the core principle at work here is the principle of separation, which is broadly affirmed in verses 44-47. This is all part of establishing the holiness of the Israelites and the distinction between cleanness and uncleanness. A big part of that holiness is building rules for the Israelites to follow that make them different than the other nations of the region, of which the food laws are one part.
That's my opinion, though it doesn't really explain the choice of banned animals, because achieving a general separation could be done with any particular list. For a more specific explanation, I would either look at the "desert living" hypothesis, or simply leave this as an exercise for the reader.
We can further see that these are ceremonial laws because of the keyword "unclean" which is repeated many times in verses 24-28. However, it is fairly mild because if you touch any of them or their dead bodies you are only unclean until evening. No sacrifice is required. There is no restitution stated for eating them, presumably because it was expected nobody would do it. Verse 40 describes what happens if you eat a dead animal "which you have for food", i.e. clean. Even then, if the animal dies without being properly slaughtered, it makes you unclean to eat it.
I thought it was interesting how verses 32-38 show that the intrinsic uncleanness of the dead animals can be passed on to jars, pots, etc of the people. This is a parallel to how the holiness of the sin offering is transferred to the pots and pans in which it is cooked (Lev 6). We can see that any ceremonial status, both positive and negative, can be transferred to anything that touches that holy or unclean object/thing/animal. This is yet another reason for the principle of separation: since uncleanness is so easily transferred, the people must be vigilant to stay far away from such things if they are to approach the LORD.
Lastly, when it says that "you shall be holy, for I am holy", this is reminiscent of Genesis 1, when man was created in the image of God. God is seeking to train the Israelites to follow his paths and live in holiness, that they can approach him and not be destroyed by his holiness. We should not forget the example of Nadab and Abihu who were destroyed by the fire from the LORD's presence when they did not honor the LORD and follow his laws.