In this chapter, the LORD details the construction of the altar of incense, the washing basin, and gives the recipes for the holy anointing oil and incense.
Starting with the altar of incense, we can see that it is going into the tent of meeting, because it is covered with gold. Verse 6 confirms that it is to be placed "in front of the veil", which I'm fairly sure means that it's in the outer portion, the "holy place", and not the inner portion, the "holy of holies". The text says the priest has to burn incense every day, but in other places it is stated that the priest only enters the holy of holies once a year, so it could not have been in the holy of holies. The altar of incense is much smaller than the bronze altar for offerings which is outside of the tabernacle. This makes sense, because it takes a lot less space to burn some incense than a whole ram.
I think it's interesting that this altar also has horns, and just as the horns of the bigger altar are covered in blood when it is consecrated, the horns of this smaller altar are to be painted with blood once a year. The only annual sin offering I can think of is the Passover, but that involves the sacrifice of many animals and not just one. So I am pretty sure v. 10 is referring to a sacrifice which has not yet been instituted (i.e. a slight anachronism). I believe this sin offering is instituted later in the Pentateuch.
The LORD also institutes "perpetual incense before the LORD throughout your generations," that in parallel with the everburning lampstand, there should be everpresent incense offered on the altar of incense. There is a third "everpresent" we haven't reached yet, which will relate to the last object in the holy place, the "table of showbread".
These instructions are so specific and so peculiar, pretty much every teacher both Jewish and Christian has their own interpretation of the significance of the incense or the burning lampstand. I mean, it's as if I commanded someone to plant a big fork in their backyard and to periodically clean it off, except instead of me, it's God. It's not the sort of thing that naturally suggests a meaning, and yet by its placement in the text and in the biblical traditions, it almost certainly has one. The cynical or non-religious jump on points like these (much as they jump on other parts of the Pentateuch) as evidence for the irrefutable confusion and meaninglessness of the bible, and yet I believe the complexity and subtlety of the bible gives the lie to the atheists' assertions.
Yet the text here does not state a meaning for these symbols (burning lampstand, burning incense), leaving us somewhat at a loss. Nevertheless, I am confident in my foreknowledge of the later books of the bible that these symbols will appear again, albeit very infrequently, and when they do, we will be given evidence of their proper interpretation. I encourage my reader to ponder these symbols and how you interpret them, just as its ancient readers must have pondered them until the days of the NT when we are given some vital clues as to their proper meaning. The third symbol (related to the table of showbread) will be partially elucidated in Deuteronomy, so we don't have to go as far for that one.
Moving on, the LORD establishes a census tax which is to pay for "the service of the tent of meeting". Unlike the earlier contribution for the construction of the tabernacle (a one-time offering largely paid for with Egyptian wealth), this is a mandatory tax that is instituted for all generations. The text doesn't specify what the funds are used for, but we can imagine it includes upkeep and repair, as well as paying for the animal sacrifices, oil for the lampstand, and the burning incense.
The census is called "atonement money", so it appears this is another type of atonement, along with the Passover. It is also similar to the Passover in that everyone must sacrifice equally. For the Passover, it was stated that everyone should slaughter lambs in accordance with what they would eat and the number of their household. Verse 12 also says this is to prevent a "plague" from breaking out when they take a census. There are two aspects to this. First, the word "plague" is the same Hebrew, "negeph", as we saw in Ex 11:1 and 12:13 to describe the death of the firstborn. So just as the Passover was the atonement for the Hebrews during that plague, the offering of atonement money is the "passover" for the Hebrews whenever they perform a census. The second aspect is that of constraining pride. Basically, whenever the Israelites perform a census, it is a sort of pride in demonstrating their own strength (in numbers). Also, it is a kind of challenge to the LORD's promise, that the descendants of Abraham would number as the stars in the sky. By counting themselves, it's sometimes treated as a challenge to that promise, like the Israelites don't believe the LORD so they want to count and see. Either way, taking a census is considered risky, and should only be done when accompanied by atonement.
Next the LORD directs the construction of the washing basin. It is made out of bronze, which is consistent with its position outside of the tabernacle. That the priests must wash before ministering is similar to earlier commands, like when Moses commanded the people to wash their clothing before meeting the LORD in Ex 19:10, and when the priests were washed before their consecration in Ex 29:4. In my opinion, the command to wash is a corollary of the earlier command for Moses to remove his shoes when treading on holy ground (Ex 3:5). As I explained there, you remove your shoes on holy ground because Moses, like all the servants of the LORD, are supposed to be in fellowship and proximity to the LORD. Moses is called into the cloud on the mountain because he is shielded and healed from the curse of Adam by the Abrahamic covenant. The holiness that in some ways risks to kill the priests (do this or you will die, do that or you will die) is something that Moses is commanded to walk upon, because his heart is purified and sanctified.
Here, the priests are commanded to wash before ministering to the LORD for the opposite reason: the outside world, the dirt and grime, is not holy, and these influences should be washed away before approaching the LORD. So on the one hand, the people of God are to walk directly upon holy ground, but on the other hand, they are commanded to wash away the non-holy dirt that accumulates through simply living in a fallen world.
The shekel of the sanctuary, contrary to the earlier "shekel of the merchants" that we saw in Gen 23:16, was considered a fairly reliable standard. As the name implies, it was established according to a scale in the sanctuary, i.e. the tabernacle. This becomes the standard unit of currency for essentially the rest of Israel's biblical history, although the measurement of currency is never explicitly ordained by the Law of Moses (or anywhere else in the OT): it's simply a cultural tradition that, as here, is implicitly assumed.
Next, the LORD gives the formula for the "holy anointing oil", which I've heard some people try to explain as metaphors for various things, but I consider it fairly prosaic. More notable is that Moses is commanded to anoint the tent, the utensils, the altars: everything, really. This is not the first time we've seen something anointed, and I don't believe I commented on it much before, but this is yet another religious practice (like animal sacrifice, or the construction of altars) that is utilized but never explained in any meaningful way. This leaves the search for meaning up to the reader, because the author never felt he had to teach his ancient readers what the purpose of anointing is: they simply "knew".
The first instance I can think of is when Jacob poured oil on the rock of Bethel in Gen 28:18. The LORD calls this "anointing" in Gen 31:13, the Hebrew "mashach", from which we derive the transliterated Messiah, which means "anointed one". This is the same "mashach" that is present here in verse 26 and a derivative is in verse 25 to describe the "anointing oil" (Hebrew, "mishchah shemen"), and so forth throughout the chapter. The next place we see anointing is when Aaron and his sons are anointed as priests in Exodus 28:41, and now we are seeing that the entire tabernacle and everything in it should be anointed. We can also infer from verses 32-33 that there were "common" anointing oils which would be used in normal situations, similar to skin lotion today, both to protect their skin from the desert and for cosmetic reasons. We will see this appear later in the bible when covering oneself in oil is a sign of joy or normalcy.
In this case, and in the prior instances of Jacob and Aaron, the use of anointing oil is only religious, with a general theme of consecration. The idea is that Jacob consecrated the rock as a future "pillar in the house of God" and Aaron and his sons are consecrated for the ministry of the priesthood. Here, not only is the oil used for sacred purposes, but the oil mixture itself is to be considered sacred. And from a humorous perspective, I might note that this is the world's first instance of intellectual property, because what is protected here is not the physical oil, but the recipe for the oil.
So while it's clear that the purpose of anointing is to consecrate something for religious service, it's not clear to me why anointing is the act to do that. While it's easy to discern the symbolic meaning of "anointing oil" in the biblical text, it's not as clear to me why the intrinsic act of anointing would hold this meaning. One could hypothetically ponder, what if it were "splash with water" instead of "anoint with oil"? All of the internal references would still be consistent, but now it's water instead of oil: would this change the meaning of the text?
I suppose referencing oil could be an analogy to preservation, that the oil is supposed to preserve whatever is anointed from damage, just as anointing one's skin preserves it from dryness? But I'm not sure how I can relate that back to consecration. Maybe I will back-edit an explanation into this post later, because I can't think of anything interesting right now.
The incense is similar to the anointing oil in its description. In this case, the primary attribute is most likely the smell, but again it's not clear to me why this has religious significance.