In terms of SEO, organic means a natural (not paid for) ranking on a search engine's results page.
Organic ranking is what you need to aim for, since research has shown that 60-80% of all clicks to a webpage come from the organic rankings and not the paid for advertising.
SEO helps your page to climb higher up the organic rankings by making your website more desirable to the search engine.
All of the SEO principles and practices that were highlighted above are aimed at raising organic ranking.
The first page of any search engine is a great place to be, just ask Wikipedia. Research has shown that most people will rather click on an organic result than on a paid for ad. While boosting organic rank and paid for links have their pros and cons and their place in SEO, you must always strive for a great organic rank.