The turning point in "Araby" is what many critics have called the "epiphany." This is a sudden moment of insight, enlightenment, understanding, or personal growth. The narrator experiences an epiphany at the end of the story when he is at the bazaar. His epiphany is a sobering realization, leaving him disappointed and disillusioned.
Leading up to the bazaar, we learn that the narrator has a spiritual side and a romantic side. He is totally enamored with Mangan's sister. "Her image accompanied me even in places the most hostile to romance." He promises to get her something at the bazaar (Araby). To the narrator, the very notion of Araby connotes ideas of an exotic land (Arab): an "Eastern enchantment." The narrator has idealized Mangan's sister so much that he has conceived of his trip to Araby as something like a romantic crusade in her honor.
When he gets to Araby, he observes some workers who are English speakers. This destroys his notion of Araby as some roving band of Eastern merchants with exotic things to sell. The English workers are counting money. The narrator is completely disillusioned at this point. This is the turning point. He has gone from idealistic, romantic crusader to skeptical adolescent. His crusade ends with this realization that the bazaar is simply a money-making scheme. He is even angry at himself for idealizing his connection to Mangan's sister in the first place.