A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
lev 12:2WOMAN'S UNCLEANNESS BY CHILDBIRTH. (Lev 12:1-8)
If a woman, &c.--The mother of a boy was ceremonially unclean for a week, at the end of which the child was circumcised (Gen 17:12; Rom 4:11-13); the mother of a girl for two weeks (Lev 12:5) --a stigma on the sex (Ti1 2:14-15) for sin, which was removed by Christ; everyone who came near her during that time contracted a similar defilement. After these periods, visitors might approach her though she was still excluded from the public ordinances of religion [Lev 12:4].
lev 12:6the 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.
lev 12:8bring two turtles, &c.--(See on Lev 5:6). This was the offering made by Mary, the mother of Jesus, and it affords an incontestable proof of the poor and humble condition of the family (Luk 2:22-24).