Miss Brill, a British expatriate who teaches English in France, leads quite a lonesome life in her adopted country. From what the reader learns, Miss Brill has made a habit of going to the public gardens on Sundays to watch people.
While she is there, she uses her imagination to give character traits to everyone that she sees there. She compares this experience to going to the theater; she makes up stories using the people whom she sees, pretends to know them, and engages in an active, imaginary storytelling with herself.
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 stage. [...]they were acting. Even she had a part and came every Sunday.
As you can see, Miss Brill's only connection with the mainstream of society is through her imagination. She has made small connections through her job as a teacher, as a reader, and maybe even at her boarding house. However, the big society that looms in the horizon is way too big for someone who is obviously so little prepared to deal with the real world.
Therefore, the main reason why Miss Brill goes to the public gardens is, first of all, out of habit; she has made it her sole and most significant form of entertainment. Second, because she gets to enter the "real world" through a fantasy. Third, because it soothes what is definitely a terrible loneliness.
She feels happy and part of something real. It is, perhaps, a safe way to be "alone, together". For some people this may seem awkward. However, there are many people just like Miss Brill who fear the sacrifices and risks that come with making human connections.