What is the significance of ivy leaves?

In O. Henry's short story "The Last Leaf," the ivy leaves are significant because, for Johnsy, they have become a measure of her time on earth.
After two young women have moved to Greenwich Village in the hopes of becoming recognized artists, a cold winter arrives, and Johnsy, who is from the sunny and warm climate of California, falls victim to pneumonia. In a short time, she becomes considerably weakened, and she lies listlessly on her bed, "looking through the small Dutch window-panes at the blank side of the next brick house." The doctor who has examined her takes her roommate Sue into the hallway, where he asks if Johnsy has anyone for whom she wants to live ("a man, for instance?"). Sue replies, "... there is nothing of the kind." Disappointed, the doctor encourages Sue to find something to make Johnsy cling to life.
After the doctor departs, Sue takes her drawing board into Johnsy's room and begins a pen-and-ink drawing for a magazine story. She hears a low sound and hurries to Johnsy's bed. Johnsy has been counting the ivy leaves that drop from the vine in "the cold breath of the wind." Johnsy informs her friend that she has been counting the ivy leaves that have fallen off the wall, and now only five are left.

"When the last one falls I must go, too. I've known that for three days. Didn't the doctor tell you?""Oh, I never heard of such nonsense," complained Sue with magnificent scorn. "What have old ivy leaves to do with your getting well?... Don't be a goosey... Try to take some broth, now...."

Johnsy insists that she wants no broth, and she keeps her eyes fixed on the ivy vine: "There goes another....That leaves just four. I want to see the last one fall before it gets dark. Then I'll go, too." This pessimism of Johnsy's worries Sue, who tells her friend that she must go downstairs to ask Mr. Behrman to model for her. "Don't try to move 'til I come back," she orders Johnsy. Hurrying to the apartment where Mr. Behrman resides, Sue informs him that Johnsy "light and fragile as a leaf herself" might drift away if her weakened hold on life grows weaker. Hearing this, the little curmudgeon, Mr. Behrman, is outraged. Angered that such foolish thoughts would enter Johnsy's head, he protests, asking Sue why she has allowed such "silly business" to enter the girl's mind. The two go upstairs and look in on Johnsy. They peer out the window with fear: "Then they look at each other without speaking."
The next morning, Johnsy demands that Sue raise the shade. Wearily, Sue obeys. There yet clings to the brick wall one ivy leaf, and Johnsy is surprised, but she declares that it will fall that day. However, the next morning the leaf is still there, clinging to the wall. For a long time, Johnsy looks at it. Finally, she asks Sue for some broth, adding that she was wrong to have wanted to die. Sadly, it is too late when someone discovers poor Mr. Behrman who has contracted pneumonia and died in his lonely apartment. In an act of love, he went out in the winter night and painted the leaf that saved Johnsy's life onto the wall where the last one had fallen.