Incessant means continuing without stopping or pausing, often to the point of being annoying or overwhelming. When something is incessant, it just keeps going and going and going.

You might hear incessant chatter from students who won't stop talking during a lesson, or experience the incessant beeping of a smoke detector with a dying battery. Rain that falls steadily for days without a break is incessant rain. A younger sibling asking “Are we there yet?” every two minutes during a long car ride is being incessantly annoying.

The word carries a sense of weariness or frustration. While “continuous” simply means ongoing, incessant suggests that you really wish it would stop. A ticking clock is continuous, but it becomes incessant when you're trying to fall asleep and can't stop noticing it.

When something ceases, it stops. When something is incessant, it refuses to cease. Think of incessant noise, incessant complaining, or incessant questions. In each case, the repetition without pause becomes the problem.