In this chapter, the LORD establishes the ordinances of the cities of refuge and how to judge murderers.
This chapter establishes a couple different things that are related, but distinct. First, it establishes that the Levites will live in cities, and the general distribution of those cities. Second, it establishes the provision of "cities of refuge", which are to be a subset of the Levitical cities. Third, it establishes the process whereby those who accidentally kill someone may flee to a city of refuge and be protected from retributive execution. I will discuss these in order.
First, the Levitical cities. This is something that has already been foreshadowed at least once, in Lev 25:32-34, which says that the property in the cities of the Levites cannot be sold and always reverts to them in the year of the Jubilee. It didn't say what the Levitical cities were, that is described here, so hopefully my readers now understand the context of that passage. More generally, we have known for some time that the Levites did not have an inheritance in the land; their inheritance is the "tithes of the sons of Israel", though more metaphorically we could say that the inheritance of the Levites is the LORD and their service to him. This is established in Num 18:23-24 with foundations elsewhere in the Pentateuch.
Given that the Levites do not have an inheritance of land, they still need somewhere to live, and that's how the idea of Levitical cities seems to emerge. They are also given a small pastureland for their animals, but clearly the Levites are neither intended nor permitted to own large blocks of land, which would allow them to farm or raise animals. This basically prohibits them from operating in the normal Israelite economy as they are expected to service the tabernacle professionally.
This raises an interesting question: what will the Levites do once the tabernacle has been settled in the promised land? Currently their assignment is to carry the tabernacle from place to place and construct or deconstruct it as required. Once in the promised land, it is very unlikely that this kind of service will be required, and yet here (and elsewhere) provision is being made for the permanent employment under the priests. This is not a question I can address here, but consider it a loose end that will have to be tied up somewhere down the line, and we will discuss this again when the time comes.
Anyway, the Levites now have 48 cities taken from the land of the other tribes. The Levitical cities are distributed according to the size of each tribe, so that more cities are taken from the larger tribes and fewer cities are taken from the smaller ones. This is fairly consistent with how Moses distributed land to the tribes in the prior chapter, giving more land to the larger and less land to the smaller.
Another interesting aspect of the Levitical cities is that it shows a slowly emerging urbanization. The vast majority of the Israelites will dwell in the countryside, away from the cities, but this is like the first flowers of spring: cities will become larger and more important as time passes. We have seen other cities before, like Heshbon the city of Sihon, or the cities built by the Reubenites and Gadites to house their women and children. In fact, the spies in Num 13 reported that the cities in the promised land were "large" and had great walls. In such a volatile region, this is a military necessity (and the Israelites' invasion itself underlines the importance of such preparations). In the future, we will see the Israelites build many more cities to defend themselves, but their economy will always remain tied to the land.
Second, out of these 48 cities, 6 of them are cities of refuge as explained here. This was also foreshadowed when we read Ex 21:13, which says that when someone accidentally kills a person, the LORD "will appoint you a place to which he may flee". This chapter takes that and establishes in much more detail where that "place" will be and what happens to a murderer when he gets there. The cities of refuge are all taken from the Levitical cities, which is interesting. We don't really know much about the Levitical cities or have reason to think of them as being special, but since the Levites are semi-priests, I think these cities are vaguely associated with the LORD. So I think fleeing to a Levitical city has the undertone of fleeing to the LORD, or seeking divine protection as well as human.
More significantly, this helps establish the Levites as judicial administrators. The Levites would be chiefly responsible for protecting all those who seek refuge in their cities and would probably also be involved in the legal process of determining the guilt or innocence of anyone who seeks refuge. Similarly, "the manslayer" must remain in the city of refuge until the death of the high priest, which doesn't give the priests more authority per se, but it intertwines the judicial system with the religious system.
As a minor note, half of the cities of refuge go on the east side of the Jordan (v. 14). This helps to accommodate the needs of Transjordan, especially since it is a large and sparsely populated region. It also shows that administering Transjordan is going to complicate whatever system of government develops in this new homeland since any government is going to be at least partially fragmented across these two states.
Third, we are given the procedure for handling "the manslayer", a person who accidentally kills another and flees from "the blood avenger" to a city of refuge. This process is also an expansion on Ex 21:13 which says that "if [the murderer] did not lie in wait", then he may flee to a city of refuge. The key characteristic is that it must not have been pre-meditated and not malicious or intentional. This chapter expands that one verse into many, giving us a lot more detail. It is mostly self-descriptive, so I won't comment on too much. What it seems to boil down to is intent. It doesn't matter if you kill someone with iron, stone, wood or even just hitting that person with your fist. If you do it "with enmity" then you will be put to death and have no recourse to the cities of refuge.
If you kill someone accidentally (by e.g. dropping a large stone off your roof and then discovering someone was standing underneath), then you must flee to a city of refuge. You will be brought from there to "the congregation" where you are judged guilty or innocent. The "blood avenger", a relative of the murdered person, is there as your accuser and prosecutor. If you are found innocent, you are still sent back to the city of refuge where you must live until the high priest dies, and then you can return to your property (i.e. inheritance). It is unclear to me how someone would survive in the city of refuge, since the Israelites are chiefly agricultural. He would probably need to find work with the Levites, or else have relatives come and give him food. I don't really know, I imagine it must have been difficult, since the manslayer would not have had access to the tithes that sustain the Levites. Since you have to stay until the high priest dies, that could be years or even decades. This must have been very challenging.
I'm not sure if I have talked about "blood avengers" before, but basically Israel does not have a police force. There is no FBI to track down criminals. All justice is citizen justice here. How this relates to murder is that if someone kills your relative, it is your duty to track that person down and kill him. That "tracking down" thing is the "blood avenger" of this chapter. Among other things, it highlights once again the significance of familial ties, because if you get murdered, it is your family's duty to avenge your death. If you have no family or a weak family, then nobody will seek to avenge you. This shows the vast significance of family, and also the power that strong, large families have over weak ones, because if you have the protection of a large clan, then you can sometimes predate on weaker ones without retribution, unless your own family stops you (for political reasons or otherwise).
It is also very significant that Israel doesn't have a professional police force. Justice is dealt with on a personal basis and mediated through tribal elders, as we can see here and elsewhere (this is one reason why tribal elders are brought in to handle subdividing the land and the census, Num 34 and Num 1 respectively). Tribal elders are probably also expected to maintain peace within their tribes and prevent the kind of abuse I described above when strong families abuse weak ones. In fact, there was no professional police force in America until the late 19th century, early 20th century, largely coinciding with industrialization. Before that, the police force existed on a semi-professional or unpaid basis, so the police was much more closely integrated with the population being policed. My hypothesis is that as Israel urbanizes, it will also adopt more formalized legal and judicial systems, but this might not be documented in the bible.
However, just because there is no police force doesn't mean that justice is unregulated. In fact, these verses are the legal code by which the people are expected to live. That's why it's called the Law of Moses, because it literally is the law for this young nation. Today, we have "other laws" to govern such issues, so in America (and elsewhere) we do not look to the bible for judicial instructions. But the Israelites did not have "other laws"; if it's not written here, then it is not a law for them, though we have seen cultural customs show up in many places. In fact, the blood avenger is a cultural custom that is referenced here but never explained. So I shouldn't make it sound as if they were totally unregulated, but I want to make it clear to my (modern, industrialized) readers that life in ancient Israel is vastly different from modern, industrialized life. If you're reading this on the internet, then you probably do not live in a society similar to ancient Israel. :)
In conclusion, "blood pollutes the land". That's why the provisions dealing with murder are so strict. Only the shedding of blood can atone for blood. And justice is not segregated off to a professional police force: it is the responsibility of the "congregation" as a whole to "judge between the slayer and the blood avenger according to these ordinances" (v. 24).