h1 is an indicator to the search engine that you consider that blurb/content to be the most important on the page. So the h1 should be optimized for the keywords you are trying to rank for. Also, if you have a bunch of h1 tags on a single page, it can actually dilute the weight of your most important heading. I recommend using just one h1 tag on a page to keep Google from having to guess what is most important. I also recommend not using any other h tags on the page for the same reason. Don't try to rank for a bunch of keywords on one page. Instead, concentrate on one or related keywords per page and use h tags to signal to the search engine what you think is most important.

Search engines are dumb. Make everything really obvious to them.