The theme of innocence is treated in a variety of ways in Henry James's Daisy Miller. However, the focal consideration that James gives to innocence, comes in the form of the social awkwardness that Daisy displays as she mingles in the epicenter of fashionable society circles.
Daisy does not properly belong to the seasoned generations of great names and great fortunes with which she sometimes socializes. For this reason, she appears in their eyes as extremely naive, inappropriate, and often impertinent in terms of her behavior and treatment of others.
However, this is all part of the sense of innocence that Daisy instills in the reader. It is quite evident that her actions do not come out of malice, and perhaps not even out of a desire for social rebellion. The problem with Daisy is that she has not lived enough, suffered enough, nor experienced enough from life. Therefore, her lack of schema renders her unable to make better judgements regarding the propriety of things, and the expectations of a lady such as herself.
The fact that Daisy dies at a young age completes the circle of the lack of fulfillment in her life. Daisy's character comes across as one who had to "hurry up" and live. As a result, she literally rushed through life, changes, and experiences without gaining any important concepts that would have lead to her self-realization and maturity. Moreover, her death came as swiftly as her life went by; this makes the reader wonder whether there was any purpose to Daisy's life at all, in the first place. Maybe Daisy symbolizes an inevitable brush of warmth in the otherwise cold and unmoved character of Winterbourne. Perhaps that is her life's purpose, after all: to shake Winterbourne out of his frozen social constructs and infuse in him the first winds of love that he would ever feel in his life again.