The narrator is an idealistic young boy who conflates his crush on Mangan's sister with religious and/or epic importance. He plans his day around getting glimpses and opportunities to see Mangan's sister. He imagines that his daily routines are actually filled with more importance as he changes those routines into quests he performs for Mangan's sister.
These noises converged in a single sensation of life for me: I imagined that I bore my chalice safely through a throng of foes. Her name sprang to my lips at moments in strange prayers and praises which I myself did not understand.
When Mangan's sister asks him about the bazaar, Araby, the narrator sees this a a connection with her, even a sign she is trying to indicate to him. He determines to go to Araby to buy her a souvenir, but in his mind it is more like a holy grail. For the narrator, "Araby" with its reference to Arab culture and the Middle East, represented something exotic: a great destination for someone on a quest for the girl he has feelings for.
Upon arriving at Araby, the narrator is disenchanted by the nonchalant, profit-interested workers. And it is at this moment that he has an epiphany that Araby is not as exotic as he'd thought, that Mangan's sister probably had not given him a second thought, and that his quest is not nearly as epic as it had been in his mind. The story is called "Araby" because it at first represented an exotic destination of a quest and then, following the epiphany, it was the site of the narrator's disenchantment.