"Miss Brill" is an example of modernist writing in a couple of ways.  One of the ways it represents modernism is that it reflects the alienation and isolation of the individual from a social setting.  One of the critical elements of modernism is the idea that individuals can be separated from their social surroundings.  Miss Brill is not a part of the world that she believes herself to be.  She is not an active agent of this world, but rather one who is isolated and marginalized from it.  Miss Brill does not even realize that this is happening to her, thinking that somehow she is the conductor of this great symphonic recognition of social awareness.  When Virgina Woolf writes that an integral part of Modernism is the "shifting of human relations," she has articulated Miss Brill's predicament.  Miss Brill has experienced a fundamental shift of human emotions and relations when she is mocked by the young couple at the end of the story.  The "shifting" that has transpired is one where Miss Brill is on the fringes of this social order, contributing to her alienation.  Like many Modernist texts, there is no reconciliation at the end of the story.  There is little in way of unity, as Miss Brill has not been able to appropriate any sort of truth or transcendent understanding about her predicament.  Instead, she blames the fur stole for what happened.  In this, there is a modernist tendency present to reject unity and symmetry in favor of disunity and a sense of loss in human consciousness.

How is "Miss Brill" connected to the Modernist movement in literature?

One of the key aspects of Modernist literature is the use of narration to show and express the world as it is perceived by the characters themselves, including their rather bizarre thoughts and perceptions. This is known as stream-of-consciousness narration and is seen in a number of works by famous Modernists such as Virginia Woolf and James Joyce. If "Miss Brill" is analysed in a similar way, Mansfield is using exactly this technique to present to us the strange world in which Miss Brill lives, a character who the narration makes clear is able to delude herself in order to ignore the crushing loneliness that otherwise threatens to overwhelm her. Note the absurd lengths to which Miss Brill takes her perception in the following quote:

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.

The reader is allowed to see into Miss Brill's mind and her attempts to ignore her isolation and solitude. Note the way that imagining the scene as a play on a stage enables her to believe that she is noted and significant and that others care about her. Narration in Modernism seeks to expose the inner workings of characters' minds so the reader is able to see their inconsistencies and partial understanding of the world, and this is something that Mansfield achieves in the creation of this character.