The young boy who is the narrator is the protagonist. He has a crush on Mangan's sister. Mangan is a neighbor and friend of his. Every day he watches her. When going to school, he follows her and at the last minute passes her so that she sees him. It's a very normal crush, and everyone seems to relate to that from experience.
However, in trying to get her attention and win her favor, he is talked into going to Araby, which is a local religiously affiliated bazaar. Normally it wouldn't be something he would go to, but when she mentions to him that she would love to go, he says he'll go for her and get her something from there. His ultimate goal is to buy her something and win her favor in the end. He has romanticized about how things will be, and Araby plays a part in helping him achieve his goal. That is not how it ends up, but that is his goal.
The protagonist is the narrator and he is trying to get to Araby to buy a gift for his romantic interest, Mangan's sister.