I heard a Fly buzz – when I died –
The Stillness in the Room
Was like the Stillness in the Air –
Between the Heaves of Storm –
The speaker seems to be on her deathbed and telling this story at the moment of death or from beyond the grave. This follows a pattern that appears in a number of Emily Dickinson poems (see  “I died for Beauty – but was scarce” . 
 As an opening line it is unsettling — the fly reference is trivial and the buzzing will stir in readers of irritating memories. And yet death is momentous and the fly has great significance in the poem.
I heard a Fly buzz 465