What is the literary element or device in Henry James's Daisy Miller, and what is the analysis of its importance to the literary work?
Your question is a little difficult to understand since there are myriad literary devices and more than half-a-dozen literary elements [literary elements are one of two kinds of literary device: (1) literary element (required devices) and (2) literary techniques (optional devices)].
One way to answer your question is to change your article "the" to "a" and think you want one example of one literary element, in which case I might suggest the thesis of the story (which may be different from a statement of the theme of the story), which might be expressed this way: "Just as innocence and gullible naivete in personal life can bring great harm to oneself and to others, so can innocence and gullible naivete in cultural life bring great harm to oneself and to others." Daisy is an example of these characteristics on both the personal life level (her personal traits) and the cultural life level (being a nouveau riche American), and she brings great harm to herself and to others through both levels.
Another way to answer your question is to think you mean an overarching element that shapes the novel, like the element of narrative mode or the element of chronology. In this case I might say that the narrative mode is that of a frame-story with an unnamed first-person narrator telling a third-person narrative to an assumed reader: "have made him known to the reader.' Coming from a first-person narrator, the third-person narration provides a proximally close, involved limited narrator who limits point of view to Winterbourne's vision and experience of events as previously told by him to the narrator.
I hardly know whether it was the analogies or the differences that were uppermost in the mind of a young American, who, two or three years ago, sat in the garden of the "Trois Couronnes," looking about him, rather idly, at some of the graceful objects I have mentioned.
Through this mode of narration, we are focused on events through Winterbourne's presence and through his thoughts, feelings and psychological state of being. We learn some things about other characters' psychology but only through the characters' own remarks, such as when we learn about Daisy's attitude toward and opinion about Winterbourne when they first re-encounter each other in Italy: her opinion is that he was mean in Vevey, and her attitude is one of mild reprimand.
By this time Daisy had turned her attention again to Winterbourne. "I've been telling Mrs. Walker how mean you were!" the young girl announced.
The chronological element is a complicated one. This frame-story is introduced in first person as to setting and central character then told in third person through an initial flashback to what happened in an earlier time "two or three years ago," during which time a chronological chain of events--which is not broken by further flashbacks nor fragmented by dislocated flash-forwards--tells the story of Daisy and Winterbourne's ill-fated encounter before finally returning to the narrator's "present" time. In other words, once the narrator introduces Winterbourne, gives his childhood background and initiates the flashback to earlier time, events in the story of Winterbourne's enchantment with Daisy move forward in cause-and-effect chronological order.
The only other possibility your question might be asking for is the genre of the novella, which is that of Realism, which emphasizes descriptive reality in dense detail; simple characters of middle class background; and characters engaged in ordinary acts of daily living. All these elements are significant to creating the meaning, suspense, disappointment and tragedy of the story.