Some mistakes mentioned in the Torah require a sacrifice whose value depends on the financial status of the one who brings it. For example, if a litigant in money matters asked a witness to testify, and the witness refused, the litigant then asked him to swear that he knows nothing, and he swore (falsely), the witness needs to bring a sacrifice. This variable cost sacrifice is an animal in the case of sufficient means, a bird offering if he is poor, and a flour offering, if he is indigent.
The same type of sacrifice is brought by one who inadvertently entered the Temple while being spritually impure, or one who ate the meat of sacrifices in this state.
A woman who gave birth brings a male lamb if she has the means, and a pair of birds if she is poor. A spiritual leper (metzora) brings three animals (sin, guilt, and burned offerings) if he has the means, and one animal and two birds if he is poor.
Art: Fritz Paulsen - The Birthday Present