An organic install means that there was no direct spend related to that install. Essentially, a user comes across your app through an app store search, a social media post or a search engine search and decides download your app. This does not include paid search results, since those results are biased from spend.
Non-organic channels require some form of effort or spend. Some examples of non-organic channels are adwords, paid social media campaigns, email blasts, and app store ads.
When looking at your marketing channels, organic installs should be a large portion of your installs. This can be accomplished by focusing search engine and app store search optimizations. This channel can, also, be heavily influenced by other paid channels by increasing traffic, which leads to higher ranking organic search results.