Supplemental results refer to search results that only show up in the search index after the normal results. Pages go supplement either if they are considered for duplicate content or they become isolated by loosing their inbound link popularity.
Supplemental Results are a way for Google to extend their search record and also for preventing questionable pages from getting massive exposure. These are the secondary database indexes of less importance and appear after the normal results with high rankings.
Supplemental Results can be avoided by simply using fresh and quality content for every single page of your site and Google should rank it well across the broad band of keywords. Your site should also get more and more inbound linking to get it indexed and avoid being supplemented in search engines.