Forum Moderators: open
A few years ago, search engines put a lot of emphasis on the words in the H1 and H2 tags. Then the word spread about this and a lot of silly webmasters started wrapping all kinds of things in H tags -- even their entire page -- and that destroyed the value of the H tag as a relevance indicator for search engines.
And so it died away -- words in the H tags were worth no more than regular text for a while. Gradually, the search engines experimented and watched as the H tag usage on the web came back to something more sane. So now the text in an H sometimes means a bit "extra", and the dial still keeps getting turned, so sometimes it doesn't.
The best practice is to structure your document the the way the W3C says to. Sometimes the H tag text will give that text a little extra boost, and sometimes maybe not. But still the best practice is to use them, and to use them correctly.