Let's start with the easier—the explicit. Our speaker starts by saying that she literally heard a fly buzz when she died. Move to stanza two and we learn that the room gets quiet and it would seem she sees God enter her room. In stanza three she shares that she has willed away her belongings and just before her last moments, a fly interjects itself into her line of vision. In her final stanza, the speaker shares that the last thing she sees before it all goes black is the fly, with its continual buzzing.
When we look more deeply, we see our speaker sharing her struggles with the eternal life and the natural life. Through each stanza, we see her balancing both spectrums, perhaps to remind us how intrinsically tied together both worlds can be. As she wills away her keepsakes, and we assume is taking her final breaths, she is brought back to her earthly place with the fly appearing in her line of vision, ultimately blocking her first look into the afterlife. But if we go back to the first line, we can infer that our speaker is able to unshackle herself from this world because she writes "I heard a Fly buzz—when I died—". With the last portion, we learn that this poem was written post-mortem, a truly interesting perspective.