First of all we need to ask the question: What is a supplemental result? (look at the last two results for example of a supplemental result) If your site is full of them then learn now how to clean it up and get better results on Google:
A supplemental result means that that page (of your website) has duplicate content from another page on the same site, this could be title tags, meta descriptions, or the actual website content itself.
Do supplemental results hurt me on Google? Yes, they take away your ability to be ranked for more pages, and limit your ability to go after more keywords.
How do I get rid of the supplemental results? What you do is grab each group of text on a page, and throw it in quotes, and put it in the search bar of google and hit search. If it brings back another page in your same site then Google is saying that group of text is the same as the group of text on this page. So if you put in your "meta" information and it only brings back one page, then you are ok with supplemental results in regards to your meta information, but if it brought back all the pages of your website then that could be what is causing the supplemental results.
If you go through all the sections of your website (headers, footers, main content) you will probably get one of the sections bringing back multiple returns when you do this in Google. When you find this, you have found the problem and need to fix that ASAP so you can start ranking better on Google.
One last thing, most people get thrown in the supplemental results by accident on thier part. They do not understand the importance of making everypage different. Google ranks webpage not websites, and once you learn that you will not make mistakes such as having the same meta information on all pages. (or whatever the case may be in your situation with supplemental results) I hope this helps.