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Shemini (Lev. 9–11) contains two main topics: the elaborate sacrificial rites performed on the eighth day of the dedication of the Tabernacle, and the laws regarding kosher and nonkosher animals.
The first topic details the numerous sacrifices accompanying the last stages of the dedication of the shrine, which reach an intensity matched only by the yearly rites of the Day of Atonement. This is no accident, because the annual event is meant to restore the shrine to the purity it possessed on the day it was dedicated. At the end of the ceremony of sacrifice and purification performed by Aaron and his sons, the Kavod—the divine Glory, which had entered the Holiest Place of the Tabernacle (Exod. 40:34)—revealed itself to the people, and shot out a flame of fire that consumed the sacrifices on the altar. The altar fire thus merged with the divine fire.
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Since that altar flame was never allowed to go out, its perpetual presence in the midst of the camp, as a nightly glow and the cloud of smoke by day, were a sign of the divine Presence in the midst of the People, similar to the pillar of cloud and fire that had led them in the desert. The same was true of the later Temple(s). The altar fire was a larger form of the eternal light.
But the sanctified mood of the day was broken by another fiery act. 
Two of Aaron’s sons, Nadab and Abihu, offered “strange fire” ( esh zarah), and the divine fire shot out again and consumed them (Lev.
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The strange fire may have been an offering of unconsecrated incense ( cf. Ketoret zarah in Exod. 30:9); but in context the offering is condemned as one that God had not authorized ( asher lo tzivvah otam).
That seems to be the crime. All through the dedication rites, it was repeatedly stated that everything was done as God had commanded Moses. Although the prohibition, in this context, against priests drinking alcohol before serving in the shrine perhaps hints that the brothers had imbibed, Nadab and Abihu made the offering—even if well-meaning—on their own initiative. The two consuming fire events—of the sacrifices on the altar and of the miscreant sons—form a play of positive and negative, a warning that priests must be punctilious in the cult or risk death.
As God said after the tragedy: “I must be sanctified [especially] by those nearest to me”—that is, the priesthood, an office fraught with danger. The events in Leviticus 10 are a counterpart to an event at the end of the wanderings, when Moses and Aaron are condemned by God for having “not sanctified” Him (Num. 20:12), although their fate is less immediate than that of Nadab and Abihu. The names of the two sons of Jeroboam—Abijah and Nadab, who succeeded their father on the throne of the Northern Kingdom of Israel—are almost the same as the names of Aaron’s sons consumed by the fire.
Jeroboam is viewed as a sinner who turned to idolatry by setting up two calves, in Bethel and Dan, a crime close to that of Nadab and Abihu’s father, Aaron, in making the Golden Calf. The intrabiblical allusion seems to hint that priestly laxity in the legitimate cult commanded by God is equivalent to the gross idolatry of the later Northern Kingdom. There is also a deeper message, regarding the nature of holiness itself, a message relevant to the entire theological undertaking of the priestly tradition. Kedushah (holiness) is essentially a feature of the divine, the supernatural, shared by God and the other divine beings, sometimes called kedoshim.