What does Araby symbolize for the protagonist and what is he trying to achieve?
To the narrator, Araby symbolizes the beauty, mystery, and romance he longs for in his life. He lives in a dreary house on a shabby dead-end street. He escapes the drabness around him by reading a Sir Walter Scott romance and a book of French adventures and by dreaming. When he hears the name "Araby," the very word thrills him: He says, "The syllables of the word Araby . . . cast an Eastern enchantment over me." His first-love obsession with Mangan's sister melds with his vision of Araby when she speaks to him of the bazaar. He's off on a knight's romantic quest to bring her a gift from the enchanted land, only to have his dreams crushed under the weight of reality.
Araby turns out to be tawdry. It is not a place of enchantment; it is a cavernous warehouse filled with cheap goods sold by ordinary people holding banal conversations in common English accents. Stalls are closed. Two men are busy counting money. There will be no enchanting gift to present to his love, and no more romantic illusions will illuminate his life. He will remain trapped in the poverty and hopelessness of Dublin's North Richmond Street.
The boy ventures off to Araby in hopes of buying something for his "crush"--Mangan's sister. He is so disillusioned with his trip and its intent that he becomes angry with himself when he has his epiphany at the end. He realizes that he had dreamt up this idea of getting something special for this girl he likes so much. When he gets there, he sees that it's not magical. It doesn't offer the perfect gift. It's dark, almost closing down, and the only girl he speaks to doesn't really want to waste her time on him or help him. She merely asks him if she can help him out of pure obligation. He realizes all of this, and that creates the anger within him as he leaves Araby to go home empty handed.
I suppose then that Araby represents some sort of "promise land" to him, but it turns out to be just another bazaar. He's trying to win the heart of a girl, but he realizes in those last moments how silly and stupid it all was and that he'd never win her heart.