The poem describes the scene and the atmosphere at the moment when someone dies, with a weird surprise thrown in. The speaker starts by mentioning the sound of a fly, which cuts across the heavy, silent air around her deathbed.
Then the speaker leaves that image behind, and begins to talk about the room where she is dying. She tells us about the people standing around her, who are calmly preparing themselves for her final moment. She even tells us about giving away the last of her possessions, to show us that everything is truly ready.
Then, just when everything is in place and as it should be, here comes that fly. It’s an intruder, a weird, unnecessary, kind of gross little bug. This wasn’t exactly a happy poem to start with, but it was sort of peaceful. When that fly shows up, everything changes, and things get stranger and a lot less quiet and comfortable.