Leviticus 12:8

8 That if her hand find not, neither she may offer a lamb, she shall take two turtles, either two culver birds, one into burnt sacrifice, and the tother for sin; and the priest shall pray for her, and so she shall be cleansed. (But if because of poverty, her hand cannot find a lamb that she may offer, she shall take two turtledoves, or two young pigeons, one for a burnt sacrifice, and the other for a sin offering; and the priest shall pray for her, and then she shall be clean.)

Leviticus 12:8 Meaning and Commentary

Leviticus 12:8

And if she be not able to bring a lamb
As everyone was not in circumstances sufficient to be at the expense of buying a lamb for this purpose, having none of their own:

then she shall bring two turtles, or two young pigeons;
which was a kind and merciful provision for the poorer sort; since it was necessary that by them the favour received should be acknowledged, as well as the sin attending them in such circumstances should be atoned for. This being the offering brought by the mother of our Lord, shows the state of poverty in which she was; and by this, and the circumcision of her child, and the presentation of it before the Lord at the time of her purification, it appears that they were both under the law, and obedient to it:

the one for a burnt offering, and the other for a sin [offering];
Jarchi observes, that in oblations the sin offering goes before the burnt offering, for sin being atoned for, the gift was accepted; but here the burnt offering went first, the reason is not very apparent:

and the priest shall make an atonement for her, and she shall be
clean;
equally the same as if she had brought a lamb, instead of young pigeons, or turtledoves.

Leviticus 12:8 In-Context

6 And when the days of her cleansing, for a son, or for a daughter, be fulfilled, she shall bring a lamb of one year into burnt sacrifice, and a culver bird, either a turtle, for sin, to the door of the tabernacle of witnessing; and she shall give to the priest, (And when the days of her cleansing, for a son, or for a daughter, be fulfilled, she shall bring a lamb of one year for a burnt sacrifice, and a young pigeon, or a turtledove, for a sin offering, to the entrance of the Tabernacle of the Witnessing; and she shall give them to the priest,)

7 which shall offer those before the Lord, and shall pray for her, and so she shall be cleansed from the flowing (out) of her blood. This is the law of a woman that childeth male, or female (This is the law for a woman who beareth a boy, or a girl).

8 That if her hand find not, neither she may offer a lamb, she shall take two turtles, either two culver birds, one into burnt sacrifice, and the tother for sin; and the priest shall pray for her, and so she shall be cleansed. (But if because of poverty, her hand cannot find a lamb that she may offer, she shall take two turtledoves, or two young pigeons, one for a burnt sacrifice, and the other for a sin offering; and the priest shall pray for her, and then she shall be clean.)