In this chapter, the LORD designates Aaron as the high priest and describes the garments of the priestly ministry.
In my mind, the biggest implication of this chapter is with respect to the "kingdom of priests" that the LORD promised back in Ex 19. If Israel is supposed to be (or become) a kingdom of priests, they why are Aaron and his sons selected "from among the sons of Israel, to minister as priest[s]"? I think this is an important question, and I think the answer is also partially revealed by the elaborate structure that is being built to contain the ark of the covenant. That is, it is increasingly clear that access to the LORD is going to be mediated by some process that will exclude the majority of Israelites. As I defined priesthood before, it is the act of "mediating between man and God", generally for the purpose of interceding for mercy, favor or specific blessings. In general, it is the establishment of a direct relationship between the priest and God in the context of priestly ministry, cf. Adam's relationship with the LORD in Gen 2 and 3.
Since Aaron is established as priest, we can reasonably surmise that he will intermediate between the Hebrew people and the LORD, in a similar way to Moses. I previously stated that Moses is acting as a prophet, while Aaron shall act as a priest. These are two different modalities, with the priest primarily focused on intercession and mercy, while the prophet is focused more on divine direction and relating the words of the LORD. More vaguely, you can imagine the priest as being the "up-channel", speaking from the people to God, while the prophet is the "down-channel", speaking from God to the people, although these are general principles that will have exceptions (for instance, Moses relates the words of the people to God in Ex 19:8).
The priestly intermediation does not seem like a proper aspect of the Abrahamic Covenant, where Abraham (the holder of the covenant) related with God directly and had no priestly intermediary. That is why I believe that the priestly intermediary is perhaps best viewed as a temporary institution until the people come into the fullness of Ex 19:6, although on this point I admit that I do not currently have textual support. It just strikes me as contrary to the precedent set in Genesis that the holders of the covenant would not directly relate with God like Moses or Aaron are authorized to do. Verse 43 also establishes the priesthood of Aaron and his sons as a "statute forever", which expresses a permanence, but I believe that this statute, like the rest of the Mosaic Covenant, is conditional on the Hebrew's obedience to the LORD (Ex 19:5, "if you will indeed obey my voice and keep my covenant..."). This is a point that is debated by some factions within Christianity, but in my opinion it is pretty clear that the covenant is conditional on Hebrew obedience.
The next overall theme I want to mention is the increasing complexity of the covenant and the Hebrew faith. Establishing a set of moral laws and a few festivals is one thing, but now we're seeing a tremendous amount of highly detailed clothing which is mandated for the priest: the breastpiece, ephod, robe, tunic, turban and sash, each with its own particular design and significance. Contrast this with Abraham, and we were never even told what Abraham was wearing, while now the high priest Aaron has this whole regalia that he must wear "so that he will not die" (v. 35) and "so that they do not incur guilt and die" (v. 43). This is incredibly severe, although it's generally within keeping of the patriarch's expectations (consider Gen 16:13, Gen 32:30, possibly others). In some sense, given the patriarchs' expectation of death upon seeing God, the freedom of Genesis might be the exception and the restraint of Exodus be the rule. The patriarchs of Genesis certainly didn't expect to see God and live, and yet I feel that exception (seeing God yet living) is what lies at the heart of the Abrahamic Covenant, because as I have already demonstrated, the Abrahamic Covenant is chiefly portrayed as a reversal of the curse of Adam. To wit, how can someone die when seeing God if they dwell in the garden of Eden, a land of communion between man and God?
In conclusion, these seem like subtle yet important contradictions. I believe the best resolution is to view them in light of the people's general ignorance of the LORD. It's clear there is some sense in which the "holiness of God" can kill people who approach him in the wrong way, and in my estimation the LORD is trying to guide and govern this new people until they are ready to approach him in the correct way with a purified heart. I think it's fair if people want to challenge my conclusions, that we can already regard the Aaronic priesthood as a temporary institution and that the tabernacle should also be regarded as a temporary restraint on the interface between the covenantal people and God. However, those who wish to challenge my conclusions are left with an evidentiary basis they have to explain: why the Mosaic Covenant is so constrained when compared to the Hebrew forefathers, and why the interface between man and God is so constrained when the Israelites are protected from the other effects of the curse of Adam (like the plagues in Egypt, cf. Goshen principle). Lastly, one must offer an alternate explanation for the meaning and purpose of Ex 19:6, which is stated as an explicit conclusion to 19:5, "if you... keep my covenant".
Before discussing details of the garments, I want to ensure my reader understands how they all fit together. First, the priest would put on a linen tunic which is basically ancient underclothing. Next is a robe which covers most of the tunic. On top of that are two shoulder pieces which are connected by golden chains. There are two rings on the shoulder pieces, which are used to hang the breastpiece in front by a blue cord. Then the priest would wear a turban with the attached "plate of pure gold", and then the priest would wear a sash too.
Also, the materials for constructing the priestly garments are very similar to those used in the tabernacle, with a fine cloth of blue, purple and scarlet and gold predominating. From the usage of gold in these garments we can infer that they will be used primarily, if not exclusively, within the confines on the tabernacle. Later passages will explicitly confirm this.
The word ephod is a simple transliteration of the Hebrew, "ephod". This transliteration is used by most major bible translations, including the NIV, NASB, NLT and Message. We can deduce from the context that the ephod is basically a robe with two shoulder pieces. However, the precise translation of "ephod" is somewhat ambiguous, because in verse 4 it is listed separately from the robe, which implies that it is properly only the shoulder pieces. However, verse 31 uses the phrase "robe of the ephod", implying the robe might be considered part of the ephod. I don't know which is correct, but in later passages the word "ephod" is used to vaguely describe priestly ceremonial garments, possibly including other elements which are considered distinct in this chapter.
With all of that said, I would next like to emphasize the aspect of Israelite unity that we see in the priestly costume. This is first established in the two stones on the shoulder pieces, where all of the twelve tribes of Israel are listed equally and together, though in birth order (v. 10). Therefore when Aaron enters the holy place (v. 43), he bears all of the tribes of Israel before the LORD in full solidarity. We next see the unity of the sons of Israel in the twelve stones on the breastpiece. Even though they are represented by separate stones, all twelve stones are together and to the best of my knowledge, the same size. The text does not seem to imply any supremacy of one stone over another, like we saw the supremacy of Judah over his brothers in Gen 49. Before men, the tribes may be stronger or weaker, but before God they are all equal.
I think it's peculiar that v. 29 says the "breastpiece of judgment". We don't actually know what that means yet, but it will be made clear when we come to understand the Urim and Thummim (more transliterations, they respectively mean "fires", or figuratively "lights", and "perfections", in the sense of "complete", "not lacking"). These are mentioned here without explanation, but later we will see that these are used in some fashion of authorized divination. It's related to judgment because the Urim and Thummim are used to discern the will of God in judgment of various situations or people. I will discuss this more later when we see them again. The usage of the priestly garments to ascertain the will of God certainly seems like a prophetic function (since it receives from God information for the people), and I would consider this another exception to the general rule that priests are up-channels, speaking from the people to God.
Lastly, on a minor note, I had previously heard some teachers state that the color blue should be associated with the prophetic ministry. I think here we can see it is clearly associated with the priestly ministry which calls into question the prophetic association. We would expect the color blue to be associated with Moses, but so far his garments have not been described (or commanded by God). This contradicts, but does not fully disprove, the assertion that blue is a prophetic color.