In this chapter, the LORD tells the people the blessings of obedience to the covenant and the many punishments for disobedience, and the mercy that follows repentance.
Before going into detail, I will simply note that a statement of blessings and punishments is typical of Hittite suzerainty treaties, which we also saw in connection with the LORD's name in Ex 20:5-6 and Ex 34:7.
This chapter begins by commanding the Israelites to not follow the religious customs of the Canaanite peoples, who would construct sacred pillars, shaped stones (and not mentioned, sacred trees to Asherah). If the people instead follow the laws of the covenant the people would be blessed primarily by success in farming (predictable rains, a massive problem in this drought-ridden area) and by military victories. Finally, v. 11-13 establishes the LORD's dwelling (i.e. tabernacle/residence) and presence amongst them, which is the most important part of the covenant, the reversal of the curse of Adam.
The second section is the punishment for disobedience, which are approximately opposite of the blessings in the prior section. Note how much longer this section is than the blessings. We can see there are escalating stages of punishment signified by the recurring phrase "seven times more for your sins" (seven is again the number of completion or fullness, denoting the multiplication of punishment) and "...then I will act with wrathful hostility against you". All of this turns on obedience to the covenant, resulting in disease and famine (the opposite of abundant food promised before), warfare and occupation (the opposite of military victory), defeat and eventual exile from the promised land into the "lands of their enemies" (possibly the opposite of the LORD dwelling in the land with the people). Making the "sky like iron and the earth like bronze" is possibly a reference to drought or famine, but more likely is simply a metaphor for the harshness and unforgiving character of the land when it turns against them.
When v. 25 mentions "when you gather together into your cities", this is typical behavior during a military invasion, as the people will flee to the relative safety of city walls. This compounds the famine because there would be no way to gather food while besieged, with the added plague of pestilence from dwelling in close quarters. The end result of this famine is cannibalism, which is notably a violation of the covenant in itself (since humans do not satisfy the constraints of Lev 11 among other things). Verse 30 speaks of destroying high places and incense altars, which is a reference to idolatrous worship outside of the authorized tabernacle. This creates a vision of the Israelites disobeying the covenant and worshiping other gods, following the customs of the nations that lived in the land before who would worship on every high place and under every spreading tree.
Next, in v. 34-35 the author again is writing ironically when he states that the land will enjoy its Sabbaths (i.e. the Sabbath years when the land is to lie fallow), which the people did not give it. This again implicates the people of not following the laws of the covenant.
While in Gen 3 the ultimate punishment of sin is death, in this chapter the ultimate punishment of sin is being driven out of the promised land. The promised land is central to the Abrahamic covenant, so this is generally appropriate.
Finally, starting in v. 40, we are told that these curses are not final: if the people "confess their iniquity" and their "uncircumcised hearts become humble" (notable as the first usage of circumcision as a metaphorical concept), then the LORD will "remember for them the covenant with their ancestors" and will "remember the land". It doesn't state exactly what the LORD will do once he remembers these things, but I believe the implication is that when the LORD remembers the covenant, he will remember what he promised to do as part of the covenant and return the people to the land and to their promised blessings.
In conclusion, I don't particularly see the relevance of this to the broader subjects of Leviticus, other than perhaps the passing reference to the Sabbath of the land (which is related to the Jubilee of the prior chapter). Nevertheless, the author may do as he pleases and it's not my place to question this editorial decision.