Something incessant continues without interruption. When you're on a cross country flight, it's tough to tolerate the incessant crying of a baby.
In Latin, cessare means 'to stop,' so when you add the negative prefix in- you get a word meaning never stopping. A near synonym is continual, but something incessant is more relentless; ceaseless is a closer synonym. It's rare to find incessant used in a positive way. Even incessant sunshine would grow boring.
