In this chapter, Moses asks for the LORD's presence to travel with his people.
The first thing to note is that while God commands Moses to depart on the journey, they don't actually leave for some time. At this point, there are still some issues to be resolved before they can leave.
The first is that the LORD says he "will send an angel before you" as the people travel to Canaan, rather than go himself, because if he went with them, "I might destroy you on the way." I think this is a reinforcement of the holiness theme which we saw previously, relating to the tabernacle. In that case, there were many barriers placed between people and the LORD such as the tabernacle itself, the veil of separation, and the other courtyard. In addition, there were many regulations governing the priests and failure to keep these also result in death. This is in recognition that while the LORD wishes to be near the people, he possesses a holiness that is deadly to those who approach him improperly.
In this case, we have already seen the people rebel against the LORD and it was only through the intercession of Moses that the people were spared. This clearly shows, however, that the people are not holy enough to safely dwell with the LORD. Yet, we know that by the construction of the tabernacle (i.e. residence) that the LORD wished to dwell with the people and that was his original intent of the covenant. This shows that the people's sinfulness has damaged their relationship with the LORD.
The people remove all of their "ornaments" as a sign of contrition, at the LORD's request. This is, of course, a continuation of their punishment for idolatry in the last chapter.
Next is a brief interjection explaining the phrase "tent of meeting", which as I previously stated is a synonym for the tabernacle. We are told that the people would see whenever the LORD came down to meet Moses, and would stand, each man at the entrance of his tent (they did not have a permanent dwelling: just as the LORD dwells in a tent, so do his people dwell in tents). It's a short story, but I think it gives us another insight into the distance between the people and the LORD. The LORD would come down to speak to their leaders, the people would observe it, and yet they stood at a distance, just like in Ex 20:19 when the people say, Moses, tell us what to do because we cannot bear listening to the LORD directly. In both Ex 20 and here, the people are portrayed as both respectful and fearful of the LORD. These are reasonable responses, and yet it is contrasted with v. 11, "thus the LORD used to speak to Moses face to face", which is a really powerful expression of God's intention for humanity. I think the phrase "face to face" sums up much of the purpose of the covenant, in bringing a restoration of the Edenic life.
The last interesting little nugget from this vignette is that Joshua would remain in the tent after Moses left. We had already seen Joshua as the military leader of Israel against Amalek, but now he is shown in piety remaining in the presence of the LORD even after their official business is concluded. Keep this in mind when we read about Joshua in the future, because remaining in the presence of the LORD voluntarily is a portent of things to come.
Continuing on with the story, Moses objects to the LORD remaining distant from the people and he issues a series of requests of deep significance. Starting in verse 13, Moses says, "If I have found favor in your sight, let me know your ways that I may know you, so that I may find favor in your sight." This is a very interesting statement, because Moses is petitioning on the basis of his favor with the LORD, that he might earn even more favor with the LORD. It seems circular, and perhaps it is, but that's how a lot of things in the world work. (Consider gravity, a process of accretion where some block of matter attracts other matter, and that's how it gains even more gravity to attract even more matter. Here, it is favor with the LROD that leads to knowing his ways, which earns more favor, which leads to knowing his ways even more, etc.)
This helps us answer the question how Moses earned favor with the LORD in the first place: he knew and followed the "ways of the LORD". I have spoken a couple times about the ways of the LORD (see Ex 12 and Ex 4), and it's a subtle and deep topic. Much of the bible is really about teaching people the ways of the LORD and it is revealed to us through things like the covenant, the stories that we have read, and what the LORD has said to Moses. We can also learn more about God's ways in the rest of Exodus, because as Moses has requested, the LORD will teach Moses his ways.
Also, the word "know" in "know your ways" is Hebrew "yada", which means to know intimdately and deeply. For instance, when Adam has sex with Eve in Gen 4:1, it says that he "yada" her. That doesn't mean the word "yada" is supposed to be sensual or sexual, it means that sex (in the context of Adam and Eve) has an operative context of profound familiarity and awareness. This is what Moses seeks with the ways of the LORD, that he would know them in a way that strongly implies he follows them, because it is only by interaction with the ways of the LORD that he could "yada" them. I think the Amplified Bible conveys the intent very well with its parenthetical, "progressively become more deeply and intimately acquainted with You, perceiving and recognizing and understanding more strongly and clearly". That's yada.
It's interesting also that Moses says this in response to the LORD refusing to go with the people, because it appears that Moses is praying both personally for his own knowledge of the LORD, but also for the people, because if the LORD travels with the people then he will implicitly impart knowledge of the ways of the LORD to the people as well. The LORD's response is to go with the people, contrary to his earlier statement.
Moses's second objection is that without the presence of God, there is nothing to distinguish them from the other peoples. This is consistent with the principle of separation, which is that the people should be separate from the idolatrous nations to show the distinction of the LORD compared to other gods. Now Moses wants the LORD to be with them, that they might be distinct from the other nations. Note that while Moses is appealing on the basis of his personal favor: "I have found favor in your sight", he deliberately includes the Hebrew people in an attempt to transfer the favor and blessings to them as well: "I and your people". I suppose you could think of this as the second dimension of Moses's humility, that not only would he try to preserve the Hebrew nation rather than build his own nation (at the LORD's suggestion), but now he is trying to leverage his favor with the LORD to attain blessings for the people. Similarly, in verse 13 he says, "consider too, that this nation is your people". While the LORD favors Moses because of Moses's character, Moses is now appealing for the nation because they are the LORD's people, i.e. appealing to the LORD's responsibility as their sovereign lord to bless them and travel with them.
The first prayer of Moses is to (deeply) know the ways of the LORD. The second prayer of Moses is that the LORD's presence would go with him and the people. The third and final prayer of Moses is to see the glory (Hebrew, "kabod") of the LORD. I will discuss the LORD's response in a moment, but even the request is profound and instructive. There is clearly a progression here, and I also think it's fairly evident that these three prayers are interrelated, with knowledge of the ways of the LORD and experiencing the presence of the LORD leading into a true vision of the glory of the LORD.
What is the glory of the LORD? That's hard to answer, but we can learn some things from the LORD's answer in the following verses. Also, note that the Hebrew kabod has a literal meaning of weight or heaviness, which figuratively means splendor, copiousness, glory, honor or majesty. Moses, then, is asking to see the majesty of the LORD, and the LORD's response is that he would "make all my goodness pass before you, and... proclaim the name of the LORD before you." As I discussed before, when the LORD shared his name with Moses in Ex 3 (which I discussed more fully in Ex 6), that divine name is more than just an identifier, it also refers to the divine character, the nature of what God is like.
The LORD is implying that his name is a proper answer to Moses's quest for glory, which makes sense when you consider the glory of the LORD to be part of his attributes or character. This is also defined by his goodness, which is a moral attribute. When most people think of splendor or majesty, they think of the material appearance of a thing, like a majestic king sitting on a golden throne ensconced with light and surrounded by attendants. The LORD considers his glory to be his goodness, or how he favorably relates to other people in kindness. More specifically, "I will be gracious to whom I will be gracious, and will show compassion on whom I will show compassion." The glory of the LORD is grace and compassion.
I don't have too much more to say on this topic, so I'll just say the obvious: this is a pretty radical redefinition of the LORD's character when compared to the book of Genesis, where he was the God of material provision and protection, and even earlier in Exodus, where he was the God of avenged wrongs, fighting to free the Israelites from unjust bondage. In the context of the increasingly rebellious Israelite nation, I think redefining himself as a God of grace and compassion is fitting, because having forgiven their idolatry just previously, the LORD is going to have to forgive many more wrongs going forward.
Lastly, the LORD repeats that Moses cannot see his face and live, which is a theme we have seen before but this time it seems the LORD really means it. We see a peculiar anthropomorphic vision of the LORD, that his "hand" would cover Moses, whie his "glory" is passing by, and then Moses shall see his "back", but not his "face". This is strange because having just equated his glory with his character and attributes, now his glory appears to be directly equated to this definite, possibly material, and very human-like form that will "pass by" Moses. I'm not sure what to say, other than both relations are true. The LORD's glory is his character and it is also his appearance. Of all the manifestations of the LORD we have seen, this one might be the most interesting yet.