Mrs. Hale notes that the Wrights' home "never seemed a cheerful place." The County Attorney attributes this to Mrs. Wright's failures as a homemaker. But Mrs. Hale concludes that it had something to do with Mr. Wright. As Mrs. Hale put it, "But I don't think a place'd be any cheerfuller for John Wright's being in it."
Mrs. Hale also notes that Mr. Wright was miserly (Glaspell uses the term "close"). Mrs. Hale assumes Minnie never had nice clothes or money to do things and this is why Mrs. Wright kept to herself and didn't belong to the Ladies Aid.
Towards the end of the play, Mrs. Hale recalls that Minnie Foster (prior to her marriage) was beautiful. "I wish you'd seen Minnie Foster when she wore a white dress with blue ribbons and stood up there in the choir and sang." (Note that she was Minnie Foster at this time, not Minnie Foster Wright. The implication is that this version of Minnie existed prior to her marriage to Mr. Wright.)
So, Minnie Foster Wright was once a beautiful, outgoing (singing in the choir) woman who became suppressed and depressed over the course of her marriage to a miserly, uncaring, and even vengeful man. Evidence of Mr. Wright's vengeance and thoughtlessness is provided with the body of the dead bird. Perhaps the most telling character analysis within the play is when Mrs. Hale compares Minnie to a bird:
She--come to think of it, she was kind of like a bird herself--real sweet and pretty, but kind of timid and--fluttery. How--she--did--change.
Singing is the major connection between the bird and Minnie. The bird was strangled (presumably by Mr. Wright). Given that Minnie's pleasures in life had seemingly dwindled to quilting and the bird, the act of Mr. Wright strangling that bird is symbolic of strangling the last bits of enjoyment Minnie had left in her life. Although one can't condone killing the husband, it is a morbid kind of poetic justice that Minnie killed the husband in the same way he killed the bird.
Minnie was once beautiful and relatively outgoing. She became melancholy and isolated. In the end, she became a vigilante and sought revenge the only way she knew how. These three characteristics trace three phases in her life: outgoing, isolated/melancholy, vengeful.