According to Wikipedia,
"Organic search results" are listings on the 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
Therefore, while preparing an organic search listing, millions of websites are searched for the presence of relevant keyword or search phrases. Obviously the websites which show the best presence of search term(s) will come up on top in the search list. Normally, considering the user behaviour for searching, it is highly important that your website show up in top 10 of the search results and is displayed on the first page of a search engine as it is less likely that some one will visit the second page.
Now the question is how to make your website searchable organically and get it listed amongst top 10? There are multiple ways of getting it done. However, few things like content, meta tags and image optimization are some of the basic techniques to approach with. It is always better to take care of these things while developing the website. Having the right keyword or phrase and place choice can also help.
We at Ekavat, do a thorough research before making a new website and take care of these issues to make sure that Search Engine Optimisation (SEO) framework is in place. This is part of our web design process and is not charged extra.