The reference to the twittering birds is the main example of animal imagery in this story:
The notes of a distant song which someone was singing reached her faintly, and countless sparrows were twittering in the eaves.
The imagery of birds twitteering can be variously interpreted. It can symbolize the vitality that is beginning to enter Louise's life now that her husband is dead. It can suggest the excitement she feels now that she realizes that she is free. It can help make her vitality, excitement, and freedom all seem natural and beautiful. Finally, the imagery of the twittering birds can be interpreted as suggesting that life goes on, despite Brently's death.
In additon, note how Chopin carefully places the reference to the twittering birds right after a reference to the "peddler crying his wares" and a reference to "some one singing." The singing carries many of the same connotations as the twittering by the birds, while the "crying" of the peddler implies that work goes on. The noise made by the peddler is highly practical; the noise made by the anonymous singer is presumably an expression of the kind of joy that Louise herself is beginning to feel.
This sense of freedom mentioned above is felt by Mrs. Mallard--whose name is a type of duck--"creeping out the the sky, reaching toward her through the sounds, the scents, the color that filled the air." She does not stop to ask if "it were or were not a monstrous joy that held her."
After Louise learns of her husband's death, she retires to her room and sits looking out the window. Outside, she sees the birds "twittering in the eaves." The birds' song is part of the imagery of spring that Chopin develops at this point in the story. Spring represents renewal and birth, and Louise is beginning to feel this sense of freedom as she realizes what her husband's death means for her life.