Mrs. Mallard's initial reaction to the news of her husband's death is intense and tumultuous grief. However, when this initial outburst has been spent, emotionally drained, Mrs. Mallard is shown settling into an armchair, looking out the open window.
Kate Chopin begins describing this scene outdoors with the following notable sentence:
She could see in the open square before her house the tops of trees that were all aquiver with the new spring life.
Note the seasonal imagery present here, shaped by the transition from winter into spring. Indeed, she's speaking about "new spring life," a detail which contextualizes the emergence of life in the context of the winter that precedes it. Symbolically speaking, this is an important detail, given that the two seasons, winter and spring, have been traditionally associated with themes of death and rebirth.
From here, we are shown images of life untouched by the tragedy of her husband's death (although, of course, in reality Mr. Mallard is still alive, a detail that proves important in the story's conclusion). Thus, the paragraph continues:
The delicious breath of rain was in the air. In the street below a peddler was crying his wares. The notes of a distant song which some one was singing reached her faintly, and countless sparrows were twittering in the eaves.
However, when reading this passage, you should keep in mind the ever-present subtext provided by the knowledge of the winter that comes before.
Thus, this scene does thematically foreshadow and mirror the emotional journey which Mrs. Mallard will embark on. At the moment, she is feeling grief for her husband's death, but soon that grief will turn into enthusiasm, as she is energized by the realization that, as a widow, she will possess a sense of agency that she had not previously known, in her existence as a wife in this male-dominated society in which she inhabits. Thus, the symbolism of new life emerging after winter's end mirrors Louise Mallard's own epiphany that stands at the center of Kate Chopin's story and the profound enthusiasm and joy which will follow her grief and loss.