How to use HTML headers properly?

Something which is not clear in my mind when people talk about semantic html. When you use headers do you use them to mark the importance of the content or section (which is subjective sometimes, could there be more than one h1 per pages), or do you use them to mark up the structure and nesting of the elements ( like: <h1><h2><h3></h3></h2><h2><h3><h4></h4></h3></h2></h1>)

cheers buddies