At the beginning of the story, the narrator notes how efficient Elisa is at caring for the chrysanthemums; the suggestion is implied that she is capable of much more. This suggestion is fitting because Elisa does have a moment of awareness that she wants more out of herself and/or more out of her life. After talking with the traveller, Elisa considers how limited her life has become. She takes pride in the chrysanthemums, even identifies with them. The chrysanthemums symbolize Elisa: both are limited by their situation. The flowers are enclosed in a wire fence to protect them from the larger, stronger animals. Just as the wire fence limits the flowers, implying they are too delicate to survive in the open, Elisa is likewise kept (by her husband and social notions of femininity) confined to specific roles of woman and wife. Elisa stresses the flowers' strength as opposed to their beauty. The suggestion is that Elisa is more than just something pretty to look at. 

Her face was eager and mature and handsome; even her work with the scissors was overeager, over-powerful. The chrysanthemum stems seemed too small and easy for her energy. 

Elisa is invigorated by her talk with the traveler. He agrees to take some chrysanthemums to a woman down the road, the chrysanthemums escape from their wire fence prison and Elisa has a sense that she's escaped from her own limitations.