After learning that her husband is on the list of those killed in a railroad disaster, Mrs. Mallard "would have no one follow her." Having reached the privacy of her bedroom, she sits facing the window where she can look out and perceive "the new spring of life" that is in the trees and, like nature, is also aquiver in her soul. Chopin's next sentence suggests this tone of hope in a new life:
The delicious breath of rain was in the air....The notes of a distant song which some one was singing reached her faintly and countless sparrows were twittering in the eaves.
All these signs of nature--the far horizon of tree tops, the "spring of life" in the "delicious rain" and singing of voices, the twittering of birds--indicate the change that comes over the woman "with a heart trouble" whose trouble has been solved. For, the repressed Mrs. Mallard can now foresee a future, and a new future, a spring of hope. Like the outdoors that she views from her window, Mrs. Mallard feels new life burgeoning in her soul; the tone of renewal is in her as well as in nature. For the first time, with a tone of renewed hope, she can look beyond each day and see the "tree tops" and "patches of blue sky" in her future.
The quote that you have identified comes after Mrs. Mallard has received the news that her husband has been killed in a train accident. However, although at first she is filled with "sudden, wild abandonment" as the "storm of grief" sweeps through her, reflecting upon her reality in solitude, she comes to change her reaction completely. Instead of being plunged into the depths of despair, she reflects on the freedom that her husband's death has given her and how precious that is to her. As she sits in her room, she looks out of the window and sees the following sights:
She could see in the open square before her house the tops of trees that were all aquiver with the new spring life. The delicious breath of rain was in the air.
Note how the tone of this passage is full of hope and new life. It is immensely significant that the season is set in spring, symbolising rebirth and the start of a new life--both for nature and for Mrs. Mallard. The tops of the trees that are "all aquiver" foreshadows the sense of "monstrous freedom" that she is about herself to experience. Thus we can see that the passage that you identified foreshadows the kind of "re-birth" that Mrs. Mallard experiences, that is unfortunately cut too short by the return of her husband.