I answered what the quotation means in the link listed below. As for short stories that support it, John in "By the Waters of Babylon", Reverend Hooper in "The Minister's Black Veil" and Sylvia in "The White Heron would be my choices.
what the great burning mean
I think it means something surrounding making better choices in lif. One needs to think before they act or your consience will be there to haunt you. Brave people own up to the responsibility of listening to their conscience. Jane Eyre, The Crucible and Of Mice Of Men are all related to this quote. Literary elements such as action that rises, lots of irony that is dramatic and forshadowing is ever present as well.