The priest is to sacrifice one as a sin offering and the other as a burnt offering. In this way the priest will make atonement for her before the LORD for her unclean discharge.
KJV
And the priest shall offer the one [for] a sin offering, and the other [for] a burnt offering; and the priest shall make an atonement for her before the LORD for the issue of her uncleanness.
ASV
And the priest shall offer the one for a sin-offering, and the other for a burnt-offering; and the priest shall make atonement for her before Jehovah for the issue of her uncleanness.