Cessation means the complete stopping or ending of something. When there's a cessation of hostilities between two countries at war, the fighting stops. When doctors talk about smoking cessation programs, they mean programs designed to help people quit smoking entirely.

The word often suggests a deliberate, definitive end. A cessation can be complete and final: if your teacher calls for a cessation of the noisy chatter in class, she wants it to stop completely. A cessation of rainfall means the rain has ended, at least for a while.

Notice that cessation often appears in formal contexts: legal documents, medical discussions, or official announcements. You're more likely to read about the cessation of a treaty than hear someone say their video game session came to a cessation (they'd probably just say it ended or stopped).