Hypnotise is the British spelling of hypnotize. It means to guide someone into a sleep-like, very focused state called hypnosis. A stage performer may hypnotise a volunteer for a show; a helper in a clinic may hypnotise a patient as part of treatment. People also stretch the word in ordinary talk: a film hypnotises you when you cannot look away; a speaker hypnotises a room when everyone goes quiet. That looser use does not mean real hypnosis — it means the thing holds your attention so strongly it feels like a spell. In American spelling you will almost always see hypnotize with a z. Same word, same meaning; only the letter in the middle of the ending changes.