Google Supplemental Results are indexed pages that show up only after the normal results. These pages usually lack credibility because they either have duplicate content or are isolated in terms of inbound links. It happens, lets say, when you have two versions of the same website or have lots of duplicate content (read Wikipedia or DMOZ) on the site. In fact, when a considerable part of your website is non-original junk, Google might devaluate the other parts too.
The reason why Google has them on the result pages is because they add to the results without getting too highlighted. However, these results have no credibility and are rarely explored by the browsers. The issue is elaborately discussed at WMW.
Kick out of the rockbottom
If you are suffering from the Suplemental Results ailment, then don't dishearten. There is cure, as nothing on Google is permanent. However, the only complication that could be is that the source of the problem might be Google itself. But in case you want to double check that it's not your fault after all, then ensure that you dont have:
1. Duplicate websites with the same content.
2. Multiple URLs for the same webpage.
3. Too much of duplicate content. Check it with Copyscape.
4. Any orphaned pages. Get links for these pages.
After you have taken all these measures, there is nothing to worry about. It will take a short while for your pages to recover.