Organic search results are listings on search engine results pages that appear because of their relevance to the search terms, as opposed to their being advertisements. In contrast, non-organic search results may include pay per click advertising.
The Google, Yahoo! and Bing search engines combine advertising and search results on their search results pages. In each case, the ads are designed to look similar to the search results, though differ in formatting enough for readers to make distinctions between organic results and ads, such as their background colour and/or placement on the page. Further, the appearance of the ads on all major search engines is so similar to the genuine search results that a large majority of search engine users cannot effectively distinguish between them.
Because so few ordinary users (38% according to Pew Research Center) realized that many of the highest placed "results" on search engine results pages were actually ads, it became important within the search engine optimization industry to distinguish between the two types of content. As the perspective among general users was that all the results were in fact "results", the qualifier "organic" was invented to distinguish the real search results from the ads. The term was first used by Internet theorist John Kilroy in a 2004 article on paid search marketing. Because the distinction is important (and because the word "organic" has many metaphorical uses) the term is now in widespread use within the search engine optimization and web marketing industry. It is, as of July 2009, now in common currency outside the specialist web marketing industry, being used frequently by Google (throughout the Google Analytics site, for instance).
Google claims that their users click (organic) search results more often than ads, which has led them to rebut the research cited above. A Google study in 2012 found that 81% of ad impressions and 66% of ad clicks happen when there is no associated organic search result on the first page.
The same report (and others going back to 1997) by Pew shows that users avoid clicking "results" that they know to be ads.
In regards to user click activity & behavior on Google's organic search results, it is widely known that it is of course best to be on Page #1 since that is where the bulk of searchers click or find what they are looking for. According to a June 2013 study by Chitika, 9 out of 10 searchers don't go beyond Google's first page of organic search results. 
Users can prevent ads from being shown in search results, and list only organic search results, by using browser add-ons and plugins. Other browsers may have different tools developed for blocking ads.
- May/June 2004 Tracking Survey Pew Internet and American Life Project
- "New research: Organic search results and their impact on search ads". Google. Retrieved 2012-08-06.
- Research Study Shows True Worth of Google's Top Search Results. http://auctusmarketing.com/so-how-much-is-the-1-google-search-result-worth/