When you wow your teacher, you get him really excited about your three paragraph essay. To wow is to impress.
If you imagine saying, "Wow!" after tasting your friend's coconut cupcakes, you'll understand exactly what the verb wow means. When the cupcakes make you exclaim like that, they wow you. A wonderful movie will wow you, and your dad's juggling act might also wow you. The word wow is Scottish in origin, an amazed interjection from the 1500's. The verb form came along in American slang much later, in the 1920's.