Do all you can to help search engines figure out the content of your page. H tags help search engines figure out the contents of a page in the same way a table of contents helps humans figure out the contents of a body of text.
Search engines are robots. They are abstract virtual representations of human behavior and values. Human beings use tables of contents to quickly identify the contents of a large text corpus (for example, a book). Think of the robot looking at a webpage, creating an automatic table of contents based on the markup on the page (like you can do with Microsoft Word). The search engine determines the "table of contents" for the page based on the H tags written to the page. Heading tags should nest intelligently, much like a table of contents should nest concepts intelligently.
Example of how a Search Engine "sees" H tags: