In this chapter, the LORD relates to Moses the ordinances for the red heifer related to ceremonial purity.
Like many legal chapters, this chapter contains a variety of new details and extensions of laws that have been already established. In this case, this chapter is expanding upon the Levitical laws of ceremonial purity related to dead bodies (of both animals and people). There isn't any particular connection between this chapter and what happens before and after. Num 18 fits into the story pretty reasonably as a response to the Israelites' fear of judgment and wrath related to their sins and the dwelling presence of the LORD, but this chapter really doesn't have to do with anything in particular that I can tell. I have no idea why this material is presented here in Numbers rather than say, Leviticus.
Starting in verse 11, it tells us about the ceremonial impurity of anyone who touches a dead body or if someone dies in a tent. This was first expressed in Lev 5:3, though admittedly as I read it now it is not clear at all if this verse is speaking of dead human bodies or other types of human uncleanness (such as bleeding, skin diseases, etc). I will actually have to go back and edit some of my earlier posts (Lev 21, Num 6, Num 9) to clarify that the Levitical law doesn't precisely condemn going near a dead body as a source of ceremonial impurity. I had misread Lev 5:2 as referring to "unclean, dead animals", i.e. that any dead thing becomes unclean. Instead I now see that it more likely refers to "dead, unclean animals", i.e. the carcasses of unclean animals (as they are later delineated).
Rather, it does so in a very allusive fashion, first in Lev 5:2-3 (touching bodies of dead, unclean animals), and then later in Lev 21 (priests cannot go near dead bodies). Lev 21 in particular contains a fairly strong implication that going near a body results in ceremonial impurity, but does not state it. Num 6 continues with the same theme, specifically confirming in v. 7 that going near a body results in ceremonial impurity, and this is approximately repeated by Num 9.
To my surprise, the law is only clearly stated here, even though it has been inferred by all these prior references. What surprises me is that this law is very much Levitical in nature and it would have fit in extremely well with the laws governing bodily emissions, mold and skin diseases. The language and structure of these laws is very similar. The emphasis on ceremonial washing is also very similar. The obvious difference is the ritual usage of the red heifer ashes, which is the only place in the NASB bible where the phrase "red heifer" occurs (other translations may vary). So this is an unusual ritual, but the use of hyssop, scarlet string and cedar wood is nearly equivalent to the ritual cleansing of skin diseases from Lev 14. This reaffirms the similarity of this ritual and the Levitical rituals.
Most details of the ritual are pretty conventional (by OT standards); it involves slaughtering an animal and sprinkling some water to purify oneself after ceremonial impurity. One thing that's unconventional is that only a single animal is slaughtered and the ashes are to be used multiple times by various people. Ordinarily each person is required to offer a sacrifice in atonement for whatever they are atoning. So this ritual, purification from the impurity related to touching dead bodies (or bones, or graves, etc) involves just a single sacrifice, though we can hypothesize this sacrifice is repeated later when the ashes are all used.
Analyzing this chapter is somewhat challenging, since the red heifer ritual is never mentioned again. Though we can reasonably infer that it was practiced for some time, there is no textual reference to it apart from this chapter. The symbolism seems to mostly tie this in with the Levitical purification rituals, but I don't know how much meaning we can extract from that. I mean, it's red string, hyssop and cedar wood: I just don't see any meaningful pattern there. We see the color red occur twice, but that color has many possible meanings so it's difficult to pin it down to any one thing. I suppose we could say it's a thinly veiled reference to blood (and hence atonement), but we already knew that an animal sacrifice was happening, which is a direct reference to blood and atonement. Why mysteriously hint at something that is directly referenced at the same time?
I've skimmed through a few commentaries and it seems that people's opinions are all over the place; there really doesn't seem to be any particular consensus, other than that the red heifer typifies the death of Christ. But again, the same can be said for most, if not all, of the Levitical sacrifices, so I'm not sure how much we can confidently read into this chapter. Maybe I'll come back and add more later, if I think of anything substantive.