When something is unceasing, it never stops — it's endless. The unceasing sound of your neighbor's dog barking makes it especially hard to get your homework done.
To cease is to stop, so anything that's unceasing doesn't end, or at least it feels like it will never end. Time is unceasing, as is your love for your pet guinea pig. It's even more common to use this word in a figurative way: "Her unceasing efforts finally convinced her parents to buy a new TV." Your own unceasing effort in learning new vocabulary words is guaranteed to bring you success!