What is the significance of the title, The Last Leaf?

As the short story's title makes clear, the last leaf remaining on the dying ivy vine provides O. Henry's central metaphor symbolizing hope, faith and the will to live another day. Likely owing to the high fever that accompanies pneumonia, Johnsy's "morbid fancy" with the leaves' annual disappearance reflects her delusional state fixed on the idea of her own life being tied the the dying vine. Because Johnsy is described in diminutive and infantilizing terms, her fevered obsession and corresponding resignation to imminent death further her characterization as helpless and dependent on care or intervention, which she receives from the three other characters. The actual last remaining leaf, and the one Mr. Behrman paints to replace is the sum of Johnsy's will to live beyond where science can effectively help her. For Mr. Behrman, who knows that he must act the moment he sees for himself that the few remaining leaves will not survive the night, the leaf he paints for Johnsy's sake represents the culmination of his life's work and his ultimate expression of hope for the next generation of artists to surpass the dashed dreams of there elders.