The central claim of "Araby" is that if you want to escape your present situation, then you should change it instead of retreating into a fantasy world. This is the common refrain of all the stories in Dubliners, which together constitute a withering critique of the cultural paralysis of contemporary Ireland.
The unnamed boy in the story wants to escape his humdrum, shabby-genteel existence. The Araby bazaar, with its exotic-sounding name and the promise of wonderful gifts, appears to provide just such an escape for the boy. The young man has developed a massive crush on Mangan's sister; she too is a part of this fantasy world that he's built for himself. The bazaar and the young girl come together in the boy's dream world, holding out the tempting prospect of hope and excitement for a life devoid of either. By heading off to the bazaar to buy Mangan's sister a gift, the boy hopes to make all his dreams come true at once.
Sadly, that doesn't happen. The boy arrives at the bazaar too late, just as it's about to close. He feels like a fool; all his hopes and dreams suddenly lie in ruins. His fantasy world was just that—a fantasy, not in the slightest bit real. This sudden realization isn't just a source of utter disillusionment; it makes the boy's eyes burn with anguish and anger.