In this chapter, the LORD institutes the ritual cleansing of the Levites.
This chapter begins with a divine command from the LORD, speaking to Moses, for Moses to share with Aaron. The bible is full of these games of telephone or relay messages, presumably because Aaron is not present with Moses in the Tent of Meeting at the time, which is a simple and reasonable explanation. Still, I always find it amusing whenever the bible has triple or quadruple nested quotations, like "The LORD told Moses, 'Tell Aaron to tell the people, "Say to one another, 'Blah.'"'". I have made it a bit of a game to try to find the most nested quotes in the bible, and I think my record is something like four, but I don't remember where.
Anyway, the actual meaning of the LORD's command is pretty hard to figure out. What the Hebrew is saying is approximately, "the seven lamps will shine toward the front face of the lampstand", which the NASB translates "in the front of the lampstand". From the construction of the lampstand (Hebrew, "menorah"), it would seem like it should cast light equally between the front and back, unless the lamps themselves had a sort of directionality? From the depiction we see of the gold lampstand in e.g. the Arch of Titus, it appears as if the lampstand should have cast light equally fore and aft. Perhaps the command in this chapter indicates some practice where the lamps would be partially veiled. Or perhaps it is not as much a specific command for the priest to do something as a statement of the purpose of the lampstand, which is to cast light into the tabernacle, where it is facing. If this is true, the LORD is not telling Aaron how to orient the lampstand, but rather stating the purpose of the lampstand and instructing Aaron in a general sense to arrange things in accordance with that purpose.
Anyway, the bulk of this chapter is a discussion of the ritual purification and "offering" of the Levites. This is a very interesting passage to me because it phrases the dedication of the Levites as being like a "wave offering", the term used for the breast of slaughtered peace offerings in e.g. Lev 7:30, but also for some of the animals slaughtered as part of the ordination process for Aaron in e.g. Ex 29:24. In the first case, the peace offering, the wave offering is given to the priest. In the second case, the ordination sacrifice, the wave offering is burned by fire.
So the wave offering doesn't seem like a tightly defined thing, since it's used in very different situations. Literally it just means that part of the offering is "waved" before the LORD. What kind of deeper significance that might have is pretty hard to discern. In this case, the term is used metaphorically since the Levites are only "offered" in the most allegorical of ways. Allegory is surprisingly rare in the Pentateuch, because much of the language is either historical (i.e. narrative) or technical/legal. Of course, later sources (and even later in the OT and NT) interpret or re-use symbolism from the Pentateuch in metaphorical ways, but as we have seen, it is unusual for the Pentateuch to do this to itself.
Nevertheless, that's exactly what we see here, and many of the same terms and rituals from the Levitical sacrifices are present here. The whole congregation (who are "offering" the Levites) are expected to gather and lay their hands on the heads of the "offering", the Levites, and then the Levites are presented before the LORD as a wave offering. At this point, the Levites are given to the LORD, in the same sense that an offering is given to the LORD, but obviously without slaying the Levites and shedding their blood, etc.
While I normally speaking of the "laying hands on their head" as a sign of transference of guilt, it's unlikely that's what it means in this case because the Levites are not slain and remain within the camp. In this case it's possibly a sign of dedication, that the people are laying their hands on the Levites to show that they are giving the Levites to the LORD. I don't have any particular reason for believing this other than a lack of alternatives (I mean, what else could it mean?).
This is all after the Levites are purified by washing and shaving their whole bodies, of course. The "offering" of the Levites also coincides with a burnt offering and sin offering. This whole process seems analogous to the consecration of the priests in Lev 8, except less elaborate. The priests didn't have to shave their bodies, but they do have to wash before putting on the holy garments and their consecration also involved several sacrifices. So, the details are clearly different which tells us (if nothing else) that the Levites are definitely not priests.
But at the same time, the Levites are clearly dedicated to the LORD and they "make atonement on behalf of the sons of Israel" (v. 19), so they are not laymen either. They are between the status of priests and laymen, a point I have made before (and yes, unlike the Nazirite vow, only men can enter the Levitical service).
The rest of this chapter just reiterates things we were told back in Num 3. Towards the end we are told the age of service for the Levites, which is nearly but not precisely the age range for the Levitical census in Num 4, which was 30 to 50. In this chapter we are told that Levites are to enter the service at 25 and retire at 50. I don't know why there is this discrepancy, since normally the OT is very precise and consistent in its numbers and calculations. I can think of many possible answers, whether from social conventions of the time, or maybe they wanted more people in the service than they found in the census, or whatever. It is unusual, but not very important.