Google uses over a hundred different factors to help determine the RELEVANCY of a page to a given query (the more relevant a page is to a query the more likely it is to show up, presuming that page has good AUTHORITY). One of the most important relevancy factors (besides the ‘page title tag’) is the heading that appears on a given page.
Just like you or I would read a page in the newspaper and use the headings to determine what each article is about, so Google can use the headings on a web page in a similar fashion. So how come so many people either don’t use headings or use poorly focused headings? Normally for design aesthetics (it looks prettier without headings) or they are so close to the website they can’t see how clear headings are important for a new visitor.
So, why not have a quick review of the headings (and don’t forget sub-headings) on your website pages and make sure they are prominent, relevant and keyword rich? You’ll improve your SEO rankings AND do your visitors a big favour.
TECHNICAL NOTE: Google is intelligent enough to interpret a heading as being the big bit of bold text at the top of a block of text – it doesn’t HAVE to be in HTML <h1> tags.