Organic (or Natural) SEO is the process of making a website and its content highly relevant for both search engines and searchers. (In other words, a clean out of all irrelevant search terms and reviving it with the new stuff!). Successful SEO will help your website gain top positions on Google, Yahoo and MSN.
A couple of examples of Organic SEO are firstly, changing the structure of a website e.g. creating text links instead of using images - the Google robots cannot 'read' what is in the image, but they can read text. Secondly, writing the text content that will be easily read and ranked by the search engines