Final answer:
The narrator Nick Carraway meets Miss Daisy Miller, who is described as having delicate grace and confidence.
Step-by-step explanation:
The important person who the narrator in the provided excerpts, presumably Nick Carraway, meets is Miss Daisy Miller. Describing her encounter with another character, most likely Winterbourne, Daisy is portrayed as a young woman with delicate grace despite being deemed common. Her mother, Mrs. Miller, is depicted as a small and elegantly dressed woman with large diamonds but who seems disengaged from her surroundings. Daisy's audacious behavior is highlighted when she arrives at a party with Mr. Giovanelli and immediately draws attention to herself, indicating her unworried demeanor and confidence.