Commentaire sur Le Lévitique 12:6

תביא כבש, “she is to bring a sheep as an offering;” when his students asked Rabbi Shimon why the mother of the baby has to bring an offering, he answered them that it was because during the contractions preceding her giving birth she swore not again to have marital intercourse with her husband which was the reason for the pain she had to endure. This was an inappropriate oath for which she as to atone.

אל פתח אהל מועד, “to the entrance of the Tent of Meeting.” This teaches that the mother herself looks after these birds as well as sheep until then, when she hands them over to the priest. (Sifra)

That is that He commanded us that any woman after childbirth offer a sacrifice - and that is a one-year old lamb as a burnt-offering, and a young pigeon or a turtledove as a sin-offering. But if she was poor, she should offer two turtledoves or two young pigeons - one for a sin-offering and one for a burnt-offering. And she is also lacking [full] atonement until she sacrifices them, as He said, "On the completion of her period of purification, for either son or daughter, she shall bring a one-year old lamb for a burnt-offering, and a young pigeon or a turtledove for a sin-offering, etc." (Leviticus 12:6). (See Parashat Tazria; Mishneh Torah, Offerings for Those with Incomplete Atonement 1.)