In this chapter, the descendants of Jacob are enslaved in Egypt and Pharaoh tries to kill their children.
This chapter begins with a very brief genealogy, really just listing the sons of Jacob, and then offers a brief transition from the events that we just read to the events of Exodus.
In my opinion, Exodus and Genesis were written as a single unit. There are basically two perspectives on this. First, some might say that they were written separately because of the gap in the storyline. Secondly, some (like myself) would say they are written as a unit because the gap is "fairly small". Some more comments:
First, the connector passage is extremely brief, so it does not really offer any evidence that the two books are unitary. It could have easily been inserted by some later compiler to provide the necessary segue.
Second, the stories in Genesis and Exodus are relatively discrete. That is, while the patriarchs of Genesis are referenced often, there are no common characters between the two books, as Exodus begins with the death of all the patriarchs "and all their generation." However, in my opinion this is not evidence that Genesis and Exodus were written separately for two reasons: the references to the patriarchs are throughout all of Exodus and show that at the very least, Genesis was written first or the material was very well known, and it is simply good literary style to keep the stories discrete.
Third, I would strongly argue that the conclusion to Genesis is unnatural and demands a sequel, and it is strongly complemented by Exodus. That is because of the "journey down to Egypt, return to the promised land" narrative that I repeatedly emphasized. Since Genesis only contains the descent to Egypt, it is not complete, and since Exodus only contains the return from Egypt, it is not complete either. It is only by joining the two that a complete narrative is formed. In fact, for this reason I would say that Genesis and Exodus are much more closely aligned than the rest of the Pentateuch as a whole.
Next, we see that Egypt, formerly the land of deliverance, is now a land of bondage. Out of concern that the Hebrews might betray the Egyptians during a war, they decide to enslave the Israelites and restrain their power. This chapter notes that the more they are oppressed, the more they spread and multiplied, which means that the oppression was not working, since its whole point was to limit their growth and power. This is a theme that is returned upon later, in the NT book of Acts, when it is frequently noted that the disciples of Jesus are persecuted almost everywhere they go, but the church grew rapidly despite or even because of this persecution. This is historically referenced as well, with the persecution of Christians having many secular sources and descriptions all the way until the time of Constantine (~300 CE). This is another one of the Bible's counterlogical philosophies, where persecution of believers itself results in the spread of that belief. It is widely believed to still be true, as there is an objective and secularly documented growth of Christianity in (for example) China, where Christianity was long persecuted, although just as in the example of Rome, it is now slowly being accepted more and more. There are other examples you can draw from the former USSR, Indonesia, etc, although in many of these instances (including China), it is hard to document the exact growth of the Church due to the persecution thereof and the fact that many Christian churches operate underground for fear of imprisonment or other state punishments.
When Joseph first came to Egypt, he came as a slave and he was treated as a slave. Through the grace of God, he prospered and was promoted, but he was still a slave. Then, through his interpretation of Pharaoh's dream, he was finally placed to save both his family and the Egyptians from the famine. So in the time of Joseph, when Jacob and his family first came down, they were welcomed by Pharaoh as the saviors of Egypt, but now they are regarded as a dangerous threat.
The second major action the king takes to order the death of all Hebrew male infants. The logic of this order is (once again) predicated on the culture of the time, which is a subject I have dwelt much upon. Male children bear the family line of their fathers, while female children are married off into another man's family and bear their children. So if all the Hebrew males are killed, then the Hebrew females must perforce marry Egyptians, and their children would be Egyptian, not Israelite. So killing the males is sufficient to destroy or severely limit the generational growth of the Israelites.
As with the persecution and oppression of the Israelites, the killing of the sons has a NT parallel recorded in Matthew 2:16, in which Herod kills all the male children of Bethlehem under 2 years of age, unsuccessfully attempting to kill who he perceived as a future political opponent.
Many Christian theologians consider Pharaoh's command in this chapter to be a demonically inspired attempt to kill the savior of the Hebrews, Moses, just as Herod's command is an attempt to kill the savior of mankind, Jesus. While there is nothing in the text here or elsewhere to support a demonic inspiration for Pharaoh, and he would otherwise be unaware of the impending birth of Moses or what role he would play in freeing the Israelites, it is true that Moses is symbolic of the future Jesus and they both play extremely similar literary and theological roles. The NT itself makes comparisons like this, for example saying that the Israelites were "baptized into Moses" in the Red Sea (1 Corinthians 10:2), just as Christians are baptized into Christ in the NT era. There are many other such NT references to the book of Exodus, but I will try to limit my exegesis of these references until this commentary reaches the relevant NT chapters. I just share this now so that my readers understand that Christian commentaries often interpret Exodus (and Genesis and...) figuratively and draw spiritual parallels to the usually physical acts of Exodus. That is why passing through the Red Sea is interpreted figuratively into being "baptized into Moses", even though it did not involve any direct baptisms and they, in fact, passed through the water and not under it.
Anyway, the trope of "Satan attempts to murder a generation of children before a savior is born" is derived from here and Matthew 2, and this in part is the inspiration of Christian resistance to abortion, which is described as essentially a demonic attempt to kill millions of children at a time when a savior (or more accurately, a generation of saviors in a NT sense of Acts) is going to be born. In fact, the very existence of widespread abortion is taken as proof that a savior(s) is on the cusp of being born, or is perhaps already born.
In the end, the midwives refuse this command and deceive Pharaoh, and God rewards them with families as a result. Nevertheless, the threat remains as Pharaoh expands his command from beyond just the midwives to the whole people of Egypt, who are granted license to kill any male Hebrew infant they find.