It means "the desolation caused by Smaug".
In the book, this is the description given to the barren area around the Mountain, specifically to the south and west. (The map displays north to the left.)
In two days going they rowed right up the Long Lake and passed out into the River Running, and now they could all see the Lonely Mountain towering grim and tall before them. The stream was strong and their going slow. At the end of the third day, some miles up the river, they drew in to the left or western bank and disembarked. ... The next day they set out again. ... The land about them grew bleak and barren, though once, as Thorin told them, it had been green and fair. There was little grass, and before long there was neither bush nor tree, and only broken and blackened stumps to speak of ones long vanished. They were come to the Desolation of the Dragon, and they were come at the waning of the year.
The Hobbit, Chapter 11, "On the Doorstep"
