Charles Ellicott Commentary Leviticus 5:7

"And if his means suffice not for a lamb, then he shall bring his trespass-offering for that wherein he hath sinned, two turtle-doves, or two young pigeons, unto Jehovah; one for a sin-offering, and the other for a burnt-offering." — Leviticus 5:7 (ASV)

And if he be not able to bring. —The only exception to this general rule was poverty. The poor man who was unable to bring a sheep or she-goat might bring two turtledoves, as these were plentiful and cheap in Palestine . We have seen in the preceding verse that in the case of the trespass offering, as with the sin offering, the fat parts, or the choicest portion, had to be consumed on the altar, being “the bread of Jehovah,” and that the remainder was the priests’ portion.

As the fat parts of the dove, or the portion for the altar, could not be separated from the bird, and as burning it wholly would destroy the character of the trespass offering and make it into a whole burnt offering, two doves were brought. One represented the portion for the Lord, and therefore was burnt on the altar, while the flesh of the other became the officiating priest’s portion.