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.

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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.