Trustrank is a term used to describe a process search engine algorithms use to rank websites. Whether trustrank actually exists is up to debate, it's a theory of those trying to figure out how search engines like Google rank sites..

The theory goes as such, search engines employ human editors to review websites for spam. The editors then develop a core set of sites considered useful, compared to pages that would be considered spam. An example of a tusted core set site would be wikipedia.

This trust is then passed down to other sites through links from the core set sites.

A site with no links from a core set site, or one of the site it links to would have no Trustrank.