I would say that the message of "The Last Leaf" hinges around two characters: Johnsy, a young artist who is dangerously sick with pneumonia, and Behrman, an old, struggling artist still holding out hope of one day painting his masterpiece. In this story, Johnsy expects to die and is watching a vine outside her window as the leaves are blown off by the wind. She intends to die when the last leaf has been removed.
As the story continues, we find that one leaf remains on that vine, and as the leaf remains on the vine, Johnsy gains a newfound determination to live. At the end of the story, it is discovered that Behrman had painted that leaf, after which he succumbs to pneumonia.
For Behrman, what we see in this painting of the leaf is the realization of his dreams of painting a masterpiece (albeit not in the way he expected). This is not a work which will be immortalized in history, making him an artist of global renown, but its impact is actually far more precious than that, given that it has quite literally saved a person's life, inspiring in her the will to live. From that perspective, I would say that "The Last Leaf" is a celebration of life and of the preciousness of life, as well as of the ways in which an individual person can leave a powerful imprint on the people around them.