In this chapter, the LORD tells Moses laws governing personal property and various other things.
While the last chapter added real punishment to murder and disrespecting your parents, this chapter adds real punishment to theft.
Even more than the last chapter, the laws governing property largely deal with livestock and to a lesser extent, crops. Theft or death of livestock appears to be the central issue here, with various procedures depending on whether the animal was on loan to another, hired out, or stolen directly from its owner.
Other than that, I don't think there's anything remarkable about the property laws. Verse 2 establishes a "Castle Doctrine" for Israel, which is still part of modern law. The Castle Doctrine states that a person has the right to defend their home (castle) from any threatening trespasser. Verse 3 puts a limitation on the right to self defense, that one cannot kill a thief if the thief enters your home at a time when it is unlikely he would attempt to harm the victims.
Punitive damages for theft (i.e. being fined more than what was stolen, which would merely be compensatory damages) is also part of modern law, just as it is established in verses 1, 4, 7 and 9. That is, the punishment is more than just to restore the lost property, it's also to punish the thief and therefore deter the crime.
I think the "various laws" from v. 16-31 are more interesting because most of them do not have modern parallels. While these laws are grouped together, it seems unlikely that they are related to each other because the topics vary widely.
First we see that premarital sex is not socially accepted. If a man "seduces" a virgin, then bam, they are now married, unless the woman's father "absolutely refuses."
Second, we see that "sorcery" is punishable by death. The word sorceress is also translated "witch" by the KJV, but most modern translations use the term sorceress. In my opinion this is pretty nebulous, because it's not defined anywhere what exactly constitutes sorcery. While I probably shouldn't spend too much time on this, I feel like the abrupt usage of the term sorceress gives us some insight into the culture of the time. It's notable that the author did not feel any explanation was necessary, that the audience would already understand what is prohibited by the nature of their familiarity with it. On the one hand, this leaves us mystified what is prohibited, but on the other hand, it teaches us that whatever it is, it would have been commonly understood if not commonly practiced.
Fortunately, other parts of the bible and contemporary research has shown that sorcery is probably constituted of divination (reading the future from animal entrails), communicating with spirits, or pronouncing ritualistic curses or blessings to achieve desired goals. In broad terms, it is the application of what we would call "magical power" to manipulate the world.
The next question is, why was this outlawed? This has various answers, but I see two central issues related to this. The first is that sorcery is possibly related to other religions and would tempt Israelites to follow other gods, in violation of the first commandment. Nothing that I said about sorcery above mentions other gods, but I believe that the actual practice of sorcery is strongly related to the sorts of "folk religions" or cults that dominated the ancient Mideast and north Africa at the time. The second issue is that sorcery is an alternate means of power outside of the bounds of the divine covenant, and therefore it is subversive to the LORD's goals, which is unity with his people. The LORD is the divine sovereign of the Hebrew people, so the expectation is that the people would turn to him in their time of need and he would provide for them. This pattern is broken if the people can turn to other practices to influence the world and achieve their goals.
Having sex with an animal is prohibited likely because it's considered unnatural and a perversion of the natural order, which was established back in Genesis 1 during the creation of the world. This is similar to the prohibition against same-sex relations, for similar reasons. Of course, the OT does not state a reason for the prohibition, so it's mostly left as speculation on my part (and on the part of anyone who says differently).
We also see one of the first protections for the "stranger", or foreigner, "for you were strangers in the land of Egypt". The OT has numerous prohibitions against mistreating or oppressing foreigners, which is interesting because in other respects, foreigners are less protected than Israelites (see, for instance, the last chapter's notes regarding slavery). Even here in this chapter, v. 25-27 prohibit charging interest against "my people" but not prohibiting usury against foreigners. To a certain extent, these abuses fall under the category of doing wrong or oppression, but the protection for foreigners is much less specific. Historically, Jews have interpreted v. 25-27 as not prohibiting charging interest to foreigners, validating my argument.
Foreigners, widows and orphans are all grouped together in this passage because they are all vulnerable social groups. Foreigners would generally not have the land or social ties of the natives, who are protected by their family or clan. Widows and orphans are vulnerable because the father of the household was their protector in a very real sense, responsible both for materially providing for them and also physically protecting them from attackers. Without a husband/father, they are comparatively defenseless and hence the LORD affords them special protection.
The idea of verse 25 is not that the Israelites would not lend to each other (this is generally encouraged), but that they would not charge interest or fees for the loan, because typically the people seeking loans are the "poor among you" and the most vulnerable to abuse.
The other laws are pretty self-explanatory, except perhaps v. 31. It seems strange that the author would relate not eating torn flesh with being "holy men". I suppose it was considered disgraceful to do? What's clear is that the author is trying to establish social standards above what was common in their time, that Israel would be distinct from the other nations in behavior. It is that distinction which is the essence of holiness.