When a search engine returns its search results, it gives you two types: organic and paid. Organic search results are the Web page listings that most closely match the user's search query based on relevance. Also called “natural” search results, ranking high in the organic results is what SEO is all about.

Organic SEO is the phrase used to describe processes to obtain a natural placement on organic search engine results pages.

Organic search refers to the natural search engine results that appear for any given query. Organic search are those which come from the algorithm used by the search engine.

Organic SEO
 

Organic SEO is the phrase used to describe processes to obtain a natural placement on organic search engine results pages.
For example: Back links, keywords

Organic SEO (search engine optimization) is the phrase used to describe processes to obtain a natural placement on organic search engine results pages (SERPs).

Organic search engine optimization (organic SEO) refers to the methods used to obtain a high placement (or ranking) on a search engine results page in unpaid, algorithm-driven results on a given search engine. Methods such as boosting keywords, backlinking and writing high-quality content can all improve a site’s page rank. Black hat SEO methods, such as the use of keyword stuffing and link farming, can also boost organic SEO.

The natural result is called as organic result.It's not a paid services.

That means natural search Results,Organic search results are the Web page listings that most closely match the user's search query.

Organic traffic is the phrase to describe the traffic which is gained from the search engine's Serps. So it's called organic traffic.

Organic search engine optimization (organic SEO) refers to the methods used to obtain a high placement (or ranking) on a search engine results.