In Trifles, Susan Glaspell seems to use the bird to reflect upon the communication, or lack thereof, Mrs. Wright has with the outside world.
Mrs. Wright has been accused of murdering her husband. When the authorities come to gather evidence, two neighboring women also come along in order to gather some things to take to Mrs. Wright in jail.
As the men carry on their business, their callous, unsympathetic and short-sighted observations about the importance of women in a home alienate the two women; they come to understand Mrs. Wright better, and create a united front to keep any damaging evidence from falling into the hands of these foolish men.
One of the things that the women find is an empty bird cage, stuffed into a cupboard. It seems a questionable piece to find in the house until the women look in Mrs. Wright's sewing box. There they find the body of a dead canary, wrapped as if Mrs. Wright had planned to bury it in a little box.
Upon reflection, the women provide us with a clearer picture of Mrs. Wright. The house is not a cheery place, but the women agree that Mr. Wright was anything but cheery. They recognize the absence of children and the loneliness that must have haunted Mrs. Wright in having no youngsters to fill her house. They remember that Mrs. Wright had once been young and pretty, and had sung in the church choir: a much different person than the woman she has become. They recognize, also, that they could have been better neighbors; that as far as they knew, Mrs. Wright was cut off from the world, doing nothing but caring for husband and home, with no love, gentleness, or connection with him (it would seem) or the world at large.
The last piece of important information comes from the manner of the bird's death: it seems as if the bird's neck had been broken. The women assume it was done by the dead husband, and that this could well have been the reason Mrs. Wright killed him—it was the last straw for her; she snapped and strangled him in his sleep.
(Mrs. Peters recalls having her kitten murdered by a boy she knew, and at that minute she had known she could have hurt him.)
The bird symbolizes joy in the world: music and life. The bird, the women believe, would have brightened up Mrs. Wright's home and her attitude. She would have been uplifted and felt a sense of hope and renewal, especially having been closed in the house alone with an uncaring, uncommunicative husband for so long. When Mr. Wright kills the bird, he robs her of happiness and renewed expectation.
Mr. Wright's sullen disposition, as described by the women at the play's beginning, would provide a sense of the kind of marriage that existed in the now-empty house. The lack of concern by the men who are searching the house reinforce the sense that the women in this society are not appreciated as they should be: their labors are taken for granted and unacknowledged.
When the bird came into her home, Mrs. Wright probably felt more alive than she had in years. With is brutal death at the hands of her husband, she may well have felt as if he had physically harmed her and the bird. Many years in a desiccated marriage drove her to strike back and kill Mr. Wright.
Since Glaspell was mainly interested in the lives of women and the roles they were forced to play in society, the bird was symbolic of Mrs. Wright herself, and the bird cage being her marriage to Mr. Wright, as well as the home she lived in and shared with her husband. These two objects show us her repression: she was like a caged bird who wanted to be free, and therefore she killed her husband to gain that freedom.
The same goes for the lack of a telephone: as you stated, she had no communication with the outside world, which made her feel even more imprisoned and hopeless. The other two women in the story, Mrs. Hale and Mrs. Peters, find these "clues" (i.e., the bird w/the wrung neck and a knotted quilt) that point to Mrs. Wright as guilty in killing her husband, but they do not tell the sheriff or attorney because they sympathize with her and understand how she felt, them being farmwives themselves.
A good example of this is when the 3 men, upon entering from looking for "evidence", laugh at the women for discussing such "unimportant" tiny things as whether she was going to quilt the pieces or knot them and birdcages. This really shows the reader what marriages were like at the beginning of the 1900s. Men saw women as tedious and uninterested in the affairs of "important matters concerning men only", and the fact that the women are the ones who found the actual evidence and that the men just laughed it off further proves how women were not considered equals in the eyes of men.