Aren’t we talking about the purification of the woman (40 days) required by Jewish law?
1Then the LORD spoke to Moses, saying, 2“Speak to the sons of Israel, saying:
‘When a woman gives birth and bears a male child, then she shall be unclean for seven days, as in the days of her menstruation she shall be unclean. 3‘On the eighth day the flesh of his foreskin shall be circumcised. 4‘Then she shall remain in the blood of her purification for thirty-three days; she shall not touch any consecrated thing, nor enter the sanctuary until the days of her purification are completed. 5‘But if she bears a female child, then she shall be unclean for two weeks, as in her menstruation; and she shall remain in the blood of her purification for sixty-six days.
6‘When the days of her purification are completed, for a son or for a daughter, she shall bring to the priest at the doorway of the tent of meeting a one year old lamb for a burnt offering and a young pigeon or a turtledove for a sin offering. 7‘Then he shall offer it before the LORD and make atonement for her, and she shall be cleansed from the flow of her blood. This is the law for her who bears a child, whether a male or a female. 8‘But if she cannot afford a lamb, then she shall take two turtledoves or two young pigeons, the one for a burnt offering and the other for a sin offering; and the priest shall make atonement for her, and she will be clean.’” Leviticus 12:1-8 NASB
http://biblehub.com/commentaries/leviticus/12-6.htm
She shall bring a lamb of the first year.—Or, as the Margin has it, a son of his year, that is, a lamb which was within the year of its birth. This burnt offering was an expression of gratitude for the Divine mercy vouchsafed to her in the hours of sorrow and danger, or, as some ancients suggest, it was designed as a confession of impatient and reproachful thoughts harboured by the mother during her pregnancy and the time of parturition (comp. Genesis 25:22); whilst the sin offering was to atone for sinful and violent expressions which she may have heedlessly uttered in the hours of labour and agony. Though when the two sacrifices are mentioned together, the sin offering generally precedes the burnt offering (see Leviticus 5:7; Leviticus 14:31; Leviticus 15:15; Leviticus 15:30; Leviticus 16:3; Leviticus 16:5, &c.), here the burnt offering takes precedence, because it is the more costly of the two. Besides the mother after child-birth (Leviticus 12:6; Leviticus 12:8), there were three other unclean persons who had to bring a sin offering for their uncleanness: the leper (Leviticus 14:19; Leviticus 14:31), the woman that had an issue (Leviticus 15:15), and the man that had an issue (Leviticus 15:30).