The sacrifices and offerings that Moses described thus far in the law were not sufficient to cleanse all the defilement that the sins of the people created. Much sinfulness still needed covering. Therefore God appointed a yearly sacrifice that cleansed all the sins not covered by other means that the Israelites committed ignorantly (Heb. 9:7). The sacrifice of the Day of Atonement was the highest and most comprehensive of the Mosaic sacrifices.
This chapter is a theological pivot on which the whole Book of Leviticus turns. It is the climax of the first part of the book that deals with the public worship of the Israelites (chs. 1-16). The second major part of Leviticus begins at the end of this chapter and reveals the private worship of the Israelites (chs. 17-27).
The chapter begins with a reference back to chapter 10, the judgment of Nadab and Abihu (v. 1). The material in chapter 16 is legislation that God prescribed shortly after and in view of that apostasy. Chapter 10 showed how important it was for priests to approach God with due care and self-preparation; those who did not died. Chapter 16 contains information about how the high priest must behave to preserve himself from a similar fate. There is this tie to the narrative of Israel's history, but chapter 16 is also a continuation of the legislation designed to differentiate between clean and unclean contained in chapters 11-15. It is another block of legal material, though the style is quite discursive.
The Day of Atonement took place six months after the Passover. These two great festivals were half a year apart. Whereas the Passover was a day of great rejoicing, the Day of Atonement was a time of great solemnity in Israel.