In this chapter, the LORD briefly interjects with some addenda and clarifications of the covenantal law.
This chapter does not particularly fit in with the last one, once again showing the author's disregard for contiguous storytelling. Most of this chapter seems concerned with Levitical law, first by stating the requirement that every burnt offering must be accompanied by a small offering of grain, oil and wine. This was commanded in a very similar fashion in Ex 29:40 and Lev 23:13, except that both of those offerings were very special cases (the first case, the daily offerings, the second, one of the harvest festivals). In this case, the command is very broad, extending to all burnt, freewill and peace offerings. We can possibly interpolate it intends to cover all offerings of these animals.
Symbolically, I'm not sure what to say about this part. We have already seen regulations concerning grain offerings and (implicitly) oil, back in Lev 2, and that section probably also covers the grain offerings described here. Wine was discussed many times in Genesis (starting in Gen 9 with Noah), but it has not been part of the sacrificial system except in Ex 29 and Lev 23 as above. In fact, we haven't even been told what a "drink offering" is. We can infer it is similar to the grain offering, possibly with some poured out and possibly some given to the priest (in whatever proportion). As before, these components of the offering match the three traditional elements of Israeli agriculture: olive groves, vineyards and (various kinds of) grain. They are all offered so that a person might offer some of everything they grow.
As we are told many times before, the law for foreigners is the same as the law for Israelites.
Verses 17-21 discuss some sort of firstfruits offering of grain. It's not clear to me if this is supposed to be the same as the festival of firstfruits (i.e. feast of weeks). The text isn't clear, but it certainly appears as if it were so.
Next, beginning in v. 22 we are given a rough restatement of the sin offering from Lev 4. The biggest difference is that if the congregation sins, it must offering a male goat in addition to the bull prescribed in Lev 4. There have been several times we have seen a solitary male goat offered as a sin offering, so this appears to be a new principle of sorts that is being added on top of the already-established Levitical law.* I couldn't possibly tell you why these regulations are stated twice. Another addition is that anyone who commits a crime willfully has no sin offering: that person must be "cut off". I previously argued that this was implied in Lev 4, which states that the offerings are only for unintentional sin. I believe this chapter reinforces that argument and is consistent with Lev 4.
We have our second (noted) episode of Sabbath-breaking. Remember that back when the Sabbath was instituted in Ex 16, it was directly related to gathering manna (something that the people would still have to do in Num 15). On the seventh day, the people were to not gather any manna, because the Sabbath is a day of rest. The Sabbath principle is extended in Ex 20:10 to specifically state that the people should do no work. Now in Ex 16, some of the people went out to gather manna anyway, and the LORD rebukes them for "[refusing] to keep my commandments and my instructions". However, the people were not punished at that time, possibly because Ex 16 predates the covenant (formed in Ex 19-24).
Here, however, we have a solitary offender who ends up as an example to the rest of the people. I see this as another exemplary vignette along the lines of Lev 10, when Nadab and Abihu were slain for abusing their privilege as priests. Here, the purpose of the story is to reinforce the sanctity of the Sabbath, which must be obeyed by all the people at the pain of death.
Lastly, we are told that the people must wear these peculiar tassels and blue cord to signify the commandments. I don't see any particular significance in this, except that it reinforces the importance of the LORD's commands. Not like we needed a reminder.
*References: Ex 12:5, the Passover lamb must be a male goat. Each family offers one, and the Passover is a type of sin offering. Lev 9:3, a male goat sin offering for the priest. Lev 16:5, two male goats for the day of atonement. However, they are sacrificed in different ways so you could pretend that it's a "two single goat offerings". Lev 23:19, a single male goat is offered during the feast of weeks. Num 7 offers twelve male goats for sin offerings, one for each tribe.