Leviticus 21:3

And for his sister a virgin, that is nigh unto him, which hath had no husband; for her may he be defiled.

The ordinary priests were forbidden to become ceremonially defiled by taking part in the customs for disposing of the dead, with exception made only for one of the immediate family. That narrow permission included a virgin sister who was near to him and who had had no husband, for whom he might be defiled. In the judgment upon Nadab and Abihu even that family exception was withdrawn because of the heinousness of their offense.

Aaron and his remaining sons were therefore allowed no outward show of mourning and could not defile themselves for the dead. They could not follow the bodies out to the funeral, and the work of disposing of the dead had to be left to relatives outside the priesthood.

The regulation stands among the dry details of laws and regulations in Leviticus that form a mighty object lesson from God emphasizing the exceeding sinfulness of sin. Those details take on new life when seen as types of Jesus Christ. All the slain beasts point forward to the Lamb of God who takes away the sin of the world.