In "Araby," what does Mangan's sister do to make a trip to the bazaar so important to the narrator?
Mangan's sister doesn't need to do anything special to make the trip to the bazaar important to the narrator. He is so enamored of her that the fact that she simply speaks to him about the bazaar would probably be enough to make him want to go. He says,
At last she spoke to me. When she addressed the first words to me I was so confused that I did not know what to answer. She asked me was I going to Araby. I forgot whether I answered yes or no. It would be a splendid bazaar; she said she would love to go [....]. She could not go, she said, because there would be a retreat that week in her convent [....]. The light from the lamp opposite our door caught the white curve of her neck, lit up her hair that rested there and, falling, lit up the hand upon the railing.
Not only does the narrator hope to make her happy by bringing her a gift from the exotic Araby, but he describes her appearance as though she were magic, lit up, and purely beautiful. Even before she speaks to him, he thinks of himself as her champion, a hero. Just prior to their conversation, he says, "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 mentions her disappointment that she cannot go to the bazaar, she, in essence, gives him his quest.
I disagree, incidentally, that the narrator's failure to name her means that his childhood feelings for her were, in fact, silly or childish. He is unnamed as well. As the other commenter states, this is a coming-of-age story, and the narrator does lose his innocent naivety, but the namelessness of both himself and his childhood love serve to make this story feel more universal.
It is clear that this short story is a "coming of age" story where the narrator is a tender adolescent boy who is completely overcome by his Romantic ideas of love. These certainly come to focus on Mangan's sister. Note how she is described from the point of view of the narrator:
She was waiting for us, her figure defined by the light from the half-opened door... Her dress swung as she moved her body and the soft rope of her hair tossed from side to side.
Note how in this description the light that surrounds her gives her an almost angelic appearance - it is as if she has a halo. This Romantic obsession the narrator has with Mangan's sister (note how she is never named - this itself seems to show the foolishness of the narrator's feelings) clearly dominates him, as he himself expresses later on in the short story:
But my body was like a harp and her words and gestures were like fingers running upon the wires.
This sets the stage for Mangan's sister's appeal to the narrator to buy something for her, clearly placing him in the role of knight errand off to complete a dangerous quest on behalf of his beautiful lady who awaits his safe return. It is this that sets the narrator up for his epiphany at the end of the story and makes him realise his own vanity.