Consider Miss Brill's fantasies. What do they reveal about her needs and fears?
As Miss Brill sits and watches the people around her in the park, she eventually realizes that "[i]t was like a play." All of the interactions she sees, even the way the sky looks—as though it is "painted" like a set—seem, to her, like a production: a production in which she, too, plays a vital role. "No doubt somebody would have noticed if she hadn't been there; she was part of the performance after all." She comes to imagine that this is the reason she leaves for the park at the same time each Sunday—because she must be on time for the performance. Such a fantasy reveals Miss Brill's fear that she would not, in fact, be missed if she were absent. Notice that no one speaks to her; at best, they only speak of her, and not in a flattering way. In fact, for some time now, Miss Brill has practiced the art of eavesdropping, and "[s]he had become really quite expert, she thought, at listening as though she didn't listen, at sitting in other people's lives just for a minute while they talked round her."
We see, then, how unnecessary her presence is. She would not be missed at all if she failed to show up on some Sunday. Miss Brill imagines the scene to be a theatrical performance, and rather than more accurately think of herself as an audience member, she casts herself as an actress. She is clearly not an actor, though; she is only a witness to the action. Rather than accept these painful facts—that her presence is not necessary, that she really doesn't matter to anyone else at the park, that she doesn't really seem to matter to anyone—Miss Brill invents a fiction that accounts for everything in a satisfying, rather than painful, way. She needs to feel wanted, needed, and her fantasy permits this, at least temporarily.