What does "Araby" symbolize to the boy, and how is the conflict of the story resolved when he goes there?
The narrator in "Araby" conflates (combines) his religious passion with his emerging romantic and sexual desires. Note that in the beginning of the story, he shows his interest in texts related to religion and romance: The Abbot (about Mary, Queen of Scots), The Devout Communicant (dealing specifically with religion), and The Memoirs of Vidocq (the adventures of a criminal-turned-detective who inspired many writers). Vidocq turns from a criminal into a policeman. The narrator in "Araby" similarly is in a period of transition: from boy to man. He builds up this image of himself as a devout, romantic, adventurous knight whose purpose is to be a knight to Mangan's sister. He is so passionate about his devotion to her, it combines his romantic and physical desire with a kind of spiritual devotion. Therefore, his quest to "Araby" becomes much more significant than simply picking up a gift at a bazaar. For the narrator, it is as if Mangan's sister were a princess and he is off to a foreign land on a quest for her (note "Arab" in "Araby"); as if he's going to the Middle East to find and reclaim the Holy Grail itself. Araby represents the destination of a quest. It is a foreign land to the narrator; it's exotic and strange, being outside the parameters of his Dublin streets.
In the end, his aspirations of himself as knight errant and his dreams of Araby as some exotic foreign land from which he will discover his princess's grail are all destroyed when he sees the bazaar as nothing more than a profit-driven fair, run by indifferent people. He is not only upset that this fantasy has been broken by his disappointment with Araby itself. He is also upset with himself. He let himself get caught up in his own fantasy (about being this kind of knight, about Araby as this otherworldly place, and about Mangan's sister), only to be let down in the end.
Gazing up into the darkness I saw myself as a creature driven and derided by vanity; and my eyes burned with anguish and anger.
He doesn't buy anything for Mangan's sister. Instead, he leaves dejected. The conflict is resolved when he realizes, in "anguish and anger," the delusion that was his fantasy.
This story, a shortened version of a “Bildungsroman” (a story of a boy growing into a man), is Joyce’s entry into the subconscious but universal impulses of all men, a combination of simple Darwinian attraction to the opposite gender, coupled with the lure of the exotic, unfamiliar landscape of adventure. By naming the fair and the story “Araby”, Joyce implants the otherness and strangeness of the environment (especially compared to the familiar and artificial mise-en-scene of Doublin’s alleyways and streets where the hero follows Mangan’s sister and fantasizes about a different life). The delay because of his uncle’s drunken tardiness, and the struggles with money, are embodiments of the obstacles in the way of any boy’s pursuit of adulthood, here as so often portrayed by his longing for his "first love," Mangan’s sister. The fair is so unlike his imagination – closing, unwelcoming, frustrating – that he almost despairs of finding the perfect magic gift to win Mangan’s sister’s heart. Like the other short stories in Joyce’s canon, Araby is a portrait in miniature of large ideas. To him, Araby is the romantic, exotic somewhere where a boy’s dream of Fair women is realized. His experiences at the fair are much more like Joyce’s own reality -- and every man’s – non-romantic, frustrating, and only partially realized, if at all.