The Waste was a region that was located somewhere within Middle-earth.
Speculation
It is possible that the capitalization of the word Waste within the published book may have been a mistake or a last minute change by J.R.R. Tolkien or by the publisher. Robert Foster has suggested that the Waste may possibly have been another name for the Desolation of Smaug, though how he came to this conclusion is unknown.
After the Battle of Five Armies, Bard gave a large amount of gold to the Master of Lake-town to help the Lake-men. However, the Master caught the dragon-sickness, stole most of the gold and fled with it from Lake-town. After his companions had deserted him, he starved to death in the Waste, sometime between T.A. 2941 and 2949.