The verb cease means “to stop,” so ceaseless refers to something that never stops. You might listen to the ceaseless sound of crashing waves at the beach, or you could say that the Internet is a ceaseless source of information. Ceaseless can also refer to things that only seem like they go on forever; it’s often used in the phrase “seemingly ceaseless.” During a blizzard you might complain about the ceaseless snow, even though the snow will eventually stop.