Charles Ellicott Commentary Leviticus 12:8

"And if her means suffice not for a lamb, then she shall take two turtle-doves, 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 shall be clean." — Leviticus 12:8 (ASV)

And if she be not able. — As a merciful provision for those who were too poor to bring a lamb, the law permits them to bring a turtle-dove or a pigeon for a burnt offering, provided that it is the same kind of bird as the one brought for a sin offering; that is, they must either be both turtle-doves or both pigeons, and not one turtle-dove and one pigeon. Turtle-doves and pigeons were plentiful and cheap in Palestine .

It was therefore the poor woman’s sacrifice that the mother of our Lord offered when, in accordance with this commutation, she offered a pair of turtle-doves or two young pigeons as she presented herself for purification at the Temple with the child Jesus, after the prescribed term of uncleanness had ended (Luke 2:24), and the priest, after sprinkling her with the blood of the humble sacrifice, declared her cleansed.