"For [his sister], he must become impure"—Leviticus 21:3.
Priests are commanded to become ritually impure [by attending the funerals of] their next of kin. Since the Torah normally forbids priests from becoming impure through contact with a corpse, one might think that the allowance for them to attend the funeral of a relative is simply to provide them with that option, but is not compulsory. Therefore the Torah clarifies that it is mandatory. As the Talmud related that Yosef the Priest's wife died on the eve of Passover and he didn't want to become impure by attending her funeral [so that he should be able to sacrifice and eat from the Paschal Offering], so the Sages "pushed" him and forced him to become impure.
Included in this mitzvah is the general obligation that everyone – priests and Israelites alike – mourn the deaths of their next of kin. (And it is because of the priest's obligation to mourn that the Torah obligates him to attend the funeral and show his respects.) According to Torah law, the mourning period is one day [following the burial]; the Sages extended this to a seven-day period of mourning.
