There are several symbols that can be identified in this story. The first few appear together in the opening scene, as Miss Esther Porley examines herself in a mirror which has seen better days.
The silk shawl Esther is carefully arranging is one which belonged to her mother. Being silk, it is expensive, a symbol of propriety and plenty. The connection to Esther's mother also indicates that it symbolizes past times: others no longer mind venturing out into the town without wearing a shawl over their shoulders, but Esther cannot bring herself to do this. Instead, she feels compelled to wrap herself in this shawl, an indication that Esther is still bound by older conventions and feels unable to move beyond what her mother taught her was appropriate.
The shawl, however, is beginning to fray and develop "tender spots" in the silk. Because of this, Esther has to arrange it carefully so the wear does not show. We can interpret this as an indication that these older conventions are, also, beginning to wear thin: there is a limit to how long Esther can continue to cling to them. At the same time, the wear on Esther's shawl represents the wear of age on Esther herself. Esther's attempts to remain proper involve contending with various challenges, such as a "wide crack" in the pair of gloves she puts on, which requires her to hold her hand always slightly beneath the shawl, and a wave in her mirror which means she can never quite tell whether her bonnet is straight. Esther, then, is struggling to cling to older conventions and also to conceal the "cracks" which symbolize her encroaching old age and loneliness. Despite her struggles, however, she is ultimately unable to keep these things from the people around her.
Another symbol in this story is Mr Rill's "chirping bullfinch." This is an animated, vibrant creature, which Mr Rill carries with him in a cage. He brings it with him to Esther's home. The pragmatic interpretation of this is that he simply could not leave his bird unattended at home, but symbolically, we could interpret this bird as a representation of promise and vigour, a new chance or opportunity currently kept in a cage. At the end of the story, Mr Rill leaves this bird at Esther's house, and Esther herself interprets this as a symbol. Because he has left the bird with her, he will be returning. In this sense, then, the bird now represents the possibility for a new future within Esther's house: Mr Rill has symbolically offered this possibility to Esther, and she has accepted it. Like the bird, the possibility of a brighter future for the two old people is now a living thing.