Part of the beauty of this short story is that we are left to infer much about the central character, Miss Brill, and her circumstances, rather than being given information about her situation directly. This is because Katherine Mansfield tells the story using the stream of consciousness point of view, so we see the thoughts of Miss Brill as they pop into her head and are shared with us.
However, what becomes movingly clear by the end of the tale is that we are presented with a desperately lonely woman whose only joy is to go out at the same time each weekend and sit and watch those around her, listening in on their lives and appreciating the "drama" that she sees. Note what the text tells us about her thoughts concerning her weekly trip to the park:
Oh, how fascinating it was! How she enjoyed it! How she loved sitting here, watching it all! It was like a play. It was exactly like a play. Who could believe the sky at the back wasn't painted? ... 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.
Miss Brill is so lonely and isolated that she is forced to imagine this "drama" to distract herself from the barren emptiness of her life, that consists of teaching English to students, reading a newspaper to a an "old invalid gentleman" and a "dark, little room" which is described as "a cupboard." This is the kind of woman that is so lonely that having an almond in her weekly-treat of honey-cake "makes a great difference." She is a character who is only able to live life vicariously through what she sees others doing.