Another thing to add to the post above is the fact Miss Brill is lonely.
In the short story, the main character doesn't interact with all the other "players" in the theatre of the mind. She comes up with these wonderful stories but she is distant from them. At the end of the story, the reader feels a great sense of pity for Miss Brill. She comes home after the incident with the young lovers, defeated. She forgoes her honeycake treat. The fox necklet no longer has its allure. She hears someone crying and it is most likely her.
Miss Brill's epiphany in "Miss Brill" relates to her relationship to other people. It starts when she realizes she's been relating to the other people in the park as if they were characters in a play, when in reality, she's part of the "play" too. Then she listens in on the young couple, only to find they are talking about her—and treating her like she's a character in a play, for their entertainment. She's quite hurt, and so realizes the layered cruelty of the world. Her epiphany, then, is that we are all connected, but we don't all realize it—and that when we don't, we hurt one another.