Why does the author not give many details about Ms. Brill's physical appearance?

Miss Brill's lack of description is important because it allows us to use our imaginations. We know that Miss Brill is a woman, that she's a teacher, and that she wears a fur. But that's about all we really do know about her. This is a deliberate strategy on Mansfield's part. As a modernist writer, she's much more concerned with what's going on inside her characters' minds than their outward appearances. The lack of a detailed description means that we can more easily concentrate on just what it is that makes Miss Brill tick, what makes her come to the park each Sunday and act out her role in the great human drama she's constructed for herself. Indeed, the paucity of physical description allows Miss Brill to act out this role more effectively; she is very much the author of her own identity.