Miss Brill is clearly lonely. However, what she seems to want most is something slightly more complex than love or even companionship. The story follows her on a Sunday, when she follows her usual practice of going to the park and listening to the band. Many other people do the same thing, and it occurs to Miss Brill that they are all performers and that she is like an actress, an integral part of this civilized scene:
They were all on the stage. They weren't only the audience, not only looking on; they were acting. Even she had a part and came every Sunday. No doubt somebody would have noticed if she hadn't been there; she was part of the performance after all.
What Miss Brill wants, therefore, is a part to play. She wants to be a harmonious component of the Sunday promenade, one of the actors in this little performance. She thinks that she has actually achieved this, until a young couple rudely refer to her as a "stupid old thing" and make it clear that she is a ridiculous and contemptible figure in their eyes. It is their harsh dismissal of her that prevents Miss Brill from achieving the harmonious participation in the life of this French town for which she had hoped and which she believed at one point that she had achieved.