This is a great question, because the story "The Odour of Chrysanthemums" is well-known for its stunning use of visual imagery (such as the chrysanthemums, and the interplay of darkness and light) to bring out its messages, or themes, which, in this story, are primarily concerned with life, marriage, and death.
In the early part of the 20th century, when this story was published, flowers were thought by many people to have symbolic properties. The meaning of the chrysanthemum was joy and happiness, and hopes for the future. This knowledge makes the symbol of the chrysanthemum more poignant in this story, because for Elizabeth, they have taken on the meaning of disappointment and bitterness.
Elizabeth is unhappy with her husband and her life. Chrysanthemums, for her, represent all the disappointments she has experienced in life. She says, "It was chrysanthemums when I married him, and chrysanthemums when [our child was] born, and chrysanthemums the first time they ever brought him home drunk, he'd got brown chrysanthemums in his buttonhole."
When her dead husband is brought in from the mine and laid out in the parlor, chrysanthemums are also used as a symbol. One of the men bringing in his body knocks over the vase of chrysanthemums by accident. Elizabeth had put them out earlier even though they reminded her of her bitter marraige and life. The chrysanthemums symbolize her married life and all its disappointments.
Their marriage was "dead" even though her husband was still alive. In the end, even the vase of flowers just leaves an odor behind. The chrysanthemums symbolize the hope and promise that the marriage never fulfilled for Elizabeth.
Another theme in the story is the theme of light and dark. Most of the action happens in the afternoon and early evening, as the sun is going down. This symbol generally suggests death and endings. The ever-growing darkness makes a contrast with the flowers, a symbol of hope. This can be interpreted as a symbol of Elizabeth's married life, with reality slowly obscuring (darkening) the promise that the wedding crysanthemums originally promised.