In this chapter, God renews his promise to Moses and a genealogy of Moses is recorded.
After Moses's complaint in the last chapter, God responds by encouraging Moses that yes, he will indeed free the Hebrews in spite of their new difficulties. The first thing he does is reaffirm that winning the freedom of the Hebrews is a power struggle, and will be a demonstration of his power: "Now you shall see what I will do to Pharaoh; for under compulsion he will let them go, and under compulsion he will drive them out of his land."
After that, the LORD says something very interesting. He says that he did not "make himself known" to the patriarchs as the LORD, but rather as God Almighty (Hebrew, El Shaddai).
First, as a side note, verse 3 is somewhat perplexing, and leads some to claim that references to "LORD" (Hebrew YHWH or Yahweh) in Genesis are anachronistic, similar to what we saw in Exodus 3. However, I don't think this is the correct rendering, because it focuses on the words Yahweh or El Shaddai rather than looking at the deeper meaning of these names. The name of the LORD is more than just a word used to refer to him, the LORD's name in this context refers to his character and attributes. For instance, later in Exodus we see the LORD say he "will proclaim the name of the LORD before you." (Exodus 33:19) If this were referring to his literal name, LORD (or YHWH), then this sentence would make no sense because he's already shared his name YHWH with Moses. Furthermore, when God does proclaim his name, he says "The LORD, the LORD God, compassionate and gracious, slow to anger, and abounding in lovingkindness and truth; who keeps lovingkindness for thousands, who forgives iniquity, transgression and sin; yet He will by no means leave the guilty unpunished, visiting the iniquity of fathers on the children and on the grandchildren to the third and fourth generations." (Exodus 34:6) As one can see, the divine name is deliberately associated with the characteristics of the divine personality, specifically with respect to how he relates to people (grace, compassion, love and justice all deal with humanity). In this verse (back to Exodus 5:3), God says that he "appeared... as God Almighty", meaning this is the aspect in which he revealed himself, but that now he was revealing himself as YHWH. These two names denote certain characteristics which can be studied based on how they are used in the bible. In general, you can look at the usage of divine names throughout the bible (there are many, at least 10 though I forget the exact number) and how those names relate to certain attributes or aspects of God; it's an interesting subject area. In this case, El Shaddai would refer to impersonal strength, since El is a general name for God and Shaddai means almighty. In broad terms, YHWH (henceforth, LORD) is associated as the name related to God's covenantal protection of the Israelites, and is therefore more of a personal name (personal-as-in-relational). This is somewhat unexpected considering everything up until this point has actually been even more impersonal than what we saw in Genesis. I mentioned that Abraham spoke with God in the form of a man, but in Exodus 3 God appears in a burning bush, which is less relatable. I think probably the biggest thing to take from this is the aspect of God's covenantal protection of the Israelites. While God did act on behalf of Abraham and Jacob on certain occasions, most of Genesis does not involve divine miracles on behalf of the covenant holders and what miracles we do see are usually subtle. In Exodus God will reveal extremely powerful miracles that effectively destroy Egypt, on behalf of freeing the Israelites. So when put in these terms, we see that God becomes less relatable in form (man -> burning bush), but that as he morphs into this new form he takes stronger and stronger actions on behalf of Israel (subtle miracles -> plagues of Egypt), which is personal in the sense that he is acting on behalf of the people of the covenant. I think this is related to how the covenant holders of Genesis were single individuals (Abraham, Isaac and Jacob in turn) and now are a whole nation (the 2MM+ Hebrew population). When they were single individuals, God appearing as a man is fitting because he can meet with the covenant holder one-on-one. Now that there are many covenant holders, this is no longer possible so God begins to express himself in a form to which the whole nation can relate: a giant series of plagues destroying their national enemies.
As another aside, JEDP theorists hypothesize that the sections of the Pentateuch which use El (or Elohim) come from one document and the sections that use LORD (Yahweh, or from German Jehovah) come from another, and that's how you get the name of the theory: Jehovist, Elohist, Deuteronomist (another document) and Priestly (the final editor). End aside.
I have already discussed several times how Exodus differs greatly from Genesis, and that God is showing himself in a different way through the use of physical miracles in e.g. Exodus 3. Just now I have discussed the changing form of how God is presenting himself to the covenantal people. Verse 3 in this chapter also gives us a sense of progressive revelation, in keeping with what we have seen so far. The principle of progressive revelation is foundational for having a proper understanding of the bible, and in my opinion this is a point that is commonly missed. Progressive revelation means that as the bible unfolds (chronologically, not necessarily in book-order), God gives progressively more detailed or specific revelations about his nature and attributes. In this verse, the LORD states that to the patriarchs, described in Genesis, he reveals himself as God Almighty, emphasizing strength and sovereignty. We see this in many areas of Genesis, such as the God (El) of Genesis 1, creating the known universe through the raw power of his spoken command. We see it in Genesis 12 and 15 where he establishes his covenant with Abraham, a covenant in which Abraham is the vassal and God is the lord. We see it in Genesis 9 when God grants that he will no longer send floods on the earth, and we see it in Genesis 7 when he did send the flood. And so forth.
Here, in Exodus, we will see God through his relationship to Israel, and hence the emphasis here on the covenantal name, LORD.
But this is a bigger deal than just Genesis and Exodus. The notion of progressive revelation appears many more times, perhaps most significantly in the NT with the sudden revelation of the suffering servant Christ. This was previously foreshadowed in Isaiah 53 and in various ways in other places, even in Exodus with the Feast of the Passover (we will get there soon). But even the things which are foreshadowed are only predicted in general terms. When the fulfillment comes, it is often unexpected or with some other twist. Another example that I have previously mentioned is the combination of priest, prophet and king in the figure of Christ. All three of these roles are separated in the OT, but combined in the NT. So though they are present in both testaments, there is this unusual or unexpected twist in the NT which in some ways redefines the meaning even of the OT.
The idea of progressive revelation is more often a redefinition of earlier things than a bringing forth of something totally new (though that happens too). That's why I can say that, e.g. Isaac is a type of Christ, in the sacrifice of the beloved son, because the death of Christ takes the prior revelation of Isaac's near-sacrifice and expands on it and redefines it. In other words, the NT gives a progressively greater revelation on the themes of Genesis 22, by following the patterns of Genesis 22 but assigning to those patterns a new and greater meaning.
Now this is all pretty straightforward and most people get it, at least in theory. Where many people misunderstand progressive revelation is when it has to do with two big things: 1) the physical nature of the OT and 2) the role and relevance of the Law of Moses. I won't discuss these in depth here, because we will see them more going forward, so I will give brief summaries and discuss these points in more detail when it becomes convenient.
1) The OT is generally defined by the physical character of what happens. This is a very broad point so I cannot fully discuss it, but I can share some examples. The blessing of Abraham was a son (Isaac) and a land (Canaan). These are physical. The blessings of Jacob and Joseph were the dew of the heavens and the richness of the earth (Genesis 27:27-29 and Genesis 49:22-26). These are all material blessings. Elsewhere, the people of Israel are blessed with riches if they follow the LORD, and poverty and famine if they do not (among other places, Deuteronomy 28). These are physical manifestations of spiritual principles. The spiritual principles are explained and reinforced in the NT, but they are pioneered in the physical examples of the OT. This is, in part, what results in a lot of the warfare between Israel and the nations around it in Canaan and elsewhere. Many people question the bible when they see the LORD helping Israel in battle and commanding Israel to wipe out hostile nations. They think, "this is a bloodthirsty God who commands so many innocent deaths." Without discussing the cultural factors that go into all this (as I do so often), I will instead refer to the importance of progressive revelation and the physical nature of the OT. The battles of Israel against hostile nations is symbolic of the spiritual battles in the NT (for instance, Ephesians 6:12). It's progressive revelation because the way that God reveals himself to Israel, by guiding them into destroying hostile nations, is *not a full revelation of who God is*. It is a specific revelation, that is trying to reveal specific characteristics. In the case of the book of Joshua (the invasion of Canaan), the specific revelation is God as the commander of the armies of heaven, manifested by commanding the army of Israel. So while this prior revelation is valid and does represent God, it does not represent God in fullness because he is only trying to reveal part of his character. When we see later revelations, we will see that this criticism (bloodthirsty God) is incorrect. I promise to talk about all of this again later and would like to restate that I'm only providing a summary, this is not meant to be a complete exposition of this issue.
2) the role and relevance of the Law of Moses. The Law of Moses is a progressive revelation in the sense that it only applies during a certain portion of history and in certain situations such as temple sacrifices. As that time has passed, and the temple has been destroyed, the Law of Moses is now superceded by the Law of the Spirit, as described in Romans 8:2 et al. Hence it is replaced by the fuller revelations that came later, and yet many modern readers will refer to essentially obsolete passages of the Law of Moses in an attempt to discredit modern Christianity. This approach is exegetically invalid, and yet that doesn't seem to slow anybody down from repeating it over and over. Hopefully I can clear up this misconception even more when I get to the NT and discuss the Law of Grace in much more detail.
Returning to the subject of Exodus 6, we see God emphasizing his covenantal protection of the Israelites in verses 3-8, mentioning the patriarchs twice, the covenant twice and the promised land twice, summarized as "You will be my people and I will be your God." God concludes by commanding Moses to speak to Pharaoh again, and Moses replies with another self-deprecating refusal. This happens again in verses 28-30, although I believe from the structure of the text this is meant as a summary of the events, rather than a statement of some other time that it happened. This is because verses 28-30 follows the genealogy, so it's structured in such a way that it completes or concludes the genealogy.
The genealogy in this chapter is mostly directed, but contains a partial broad section (see Genesis 10 for a brief summary of my two types of genealogies). It begins with the families of Reuben and Simeon, which is in birth-order, listed oldest first. This is probably a token of respect for the older brothers before moving on to the family that the author really cares about, the children of Levi. The author then explores the Levite family tree until he reaches the family of Moses and Aaron, who we can see are three generations removed from Levi. This is much fewer that I would expect for a 400 year period, so I'm not sure how these dates can be reconciled other than suggesting that they had children very late. Unlike the earlier genealogies in e.g. Genesis 5, here it does not state how old the fathers are when they have their sons, so it's not possible to cross-reference and find a reconciliation.
The main purpose of the genealogy here, as I understand it, is to ground the events of Moses's and Aaron's lives with the prior stories of the patriarchs in Genesis. By drawing a connection between the genealogy of verses 14-25 and the events of verses 26-30, we can again see that Exodus is merely continuing the story from Genesis in Israel's redemptive history.