Jamieson, Fausset and Brown on Leviticus 12:6-8

6-8. the days of her purifying--Though the occasion was of a festive character, yet the sacrifices appointed were not a peace offering, but a burnt offering and sin offering, in order to impress the mind of the parent with recollections of the origin of sin, and that the child inherited a fallen and sinful nature. The offerings were to be presented the day after the period of her separation had ended--that is, forty-first for a boy, eighty-first for a girl.