Organic search engine optimization results are the search results that you see that are not paid (Pay-Per-Click), instead they are created organically by formatting webpages how search engines prefer combined with backlinks to a website. These 2 techniques will naturally move your website up to the 1st page of search engines like Google, Yahoo and Bing.
Organic on-page search engine optimization (SEO) is basically formatting your website pages so that they show up 1st or as close to 1st as possible on search engine such as Google, Yahoo and Bing.
Their website has better SEO than your website. They have better on-page SEO and / or more off-page SEO, i.e. Backlinks, which equal a higher Google Page Rank.