Make sure you have an H1 tag on every page of your site. On the home page it should probably be the SiteName/Brand name but for the rest of the site make appropriate to the page. I try to think of a site like a book. You only have the book name as a title once. After that the title will most likely be the chapter (Category) you are reading. And make sure you only have 1 H1 tag per page.
“Heading tags (not to be confused with the HTML tag or HTTP headers) are used to present structure on the page to users. There are six sizes of heading tags, beginning with h1, the most important, and ending with
h6, the least important.”
http://static.googleusercontent.com/external_content/untrusted_dlcp/www.google.com/en//webmasters/docs/search-engine-optimization-starter-guide.pdf Page 13.
Its also important to use your H2 tags to put more context on the page, but do not over use them.
Google uses the example of a news story where the H1 tag is used for the name of the site and the H2 tag is used for the topic of the story.
In an eCommerce site, for example a landing page, the H1 tag could be used for the Title of the Landing Page and the H2 tag could be used for the subsections of the page e.g New Releases, Best Sellers etc.