On the eighth day, following the seven days of their inauguration, Aaron and his sons begin to officiate as kohanim (priests); a fire issues forth from G‑d to consume the offerings on the altar, and the divine presence comes to dwell in the Sanctuary.
Aaron’s two elder sons, Nadav and Avihu, offer a “strange fire before G‑d, which He commanded them not” and die before G‑d. Aaron is silent in face of his tragedy. Moses and Aaron subsequently disagree as to a point of law regarding the offerings, but Moses concedes to Aaron that Aaron is in the right.
G‑d commands the kosher laws, identifying the animal species permissible and forbidden for consumption. Land animals may be eaten only if they have split hooves and also chew their cud; fish must have fins and scales; a list of non-kosher birds is given, and a list of kosher insects (four types of locusts).
Also in Shemini are some of the laws of ritual purity, including the purifying power of the mikvah (a pool of water meeting specified qualifications) and the wellspring. Thus the people of Israel are enjoined to “differentiate between the impure and the pure.”