"Cease" means "to end" or "to stop". Please cease harassing me or I will call the police. Cease and desist from downloading illegal movies over the internet or you will be blocked. "Cease to exist" means to die, or stop living. Ever since the prehistoric age, dinosaurs have ceased to exist.
We will cease fire for a peace talk. "Oi! Cease that noise, you ruffians!" the librarian yelled at the top of her lungs. It was almost like the entire village ceased to exist. I beg you to cease your nagging.