Desolation is emptiness and hopelessness. It can describe a poor, dirty, treeless town or a broken heart.
Desolation is depressing and bleak. People arriving at the scenes of natural disasters, like tornadoes, often speak about the desolation around them. They usually are talking about the destruction, but they also implying a sense of emptiness and hopelessness. Other times desolation describes bleak, ugly landscapes: cold, snowy, lonely towns in New Hampshire or hot, dusty, empty towns in Nevada. You know desolation when you see it, because you feel hollow and lonely inside.