What is the Great Burning and Destruction that is talked about in "By the Waters of Babylon"?
We actually "see" for ourselves the "Great Burning" that destroyed our civilisation in this dystopian masterpiece during the vision that John has whilst he is sleeping in one of the towers in the city. Note what John says about what he sees:
When gods war with gods, they use weapons we do not know. It was fire falling out of the sky and a mist that poisoned. It was the time of the Great Burning and the Destruction. They ran about like ants in the streets of their city - poor gods, poor gods!
We need to remember that because this story is told from the first person perspective, we see everything through John's eyes. He does not know about sophisticated military weapons, so he only describes what he sees. We can infer from his description however that "the Great Burning" and "the Destruction" were caused by advanced nuclear and chemical weaponry that brought fire down upon the world and poisonous gas.