What is an unsolicited external link, and how do organic links differ from other external links?
An unsolicited external link is a link to your web site from another web site that the owner or manager of that other web site added to their site of their own accord. It's an external link that you did not pay for or ask for.
Unsolicited external links tend to be the most valuable type of external link from a SEO (search engine optimization) perspective. Since these external links are added to another site without your request, these links demonstrate to the search engines the value of your web site and your content, and improve your web site's ranking in "natural search."
These organic external links also tend to be in the context of the page or in the middle of the content, so the search engines can garner more information about the "relevance" of your web page or web site based on the content this external link is in.
With any external link, but particularly with unsolicited external links, the higher the rank of the web page you are linked from, the greater the SEO benefit of the link itself.