What does it mean for a Search Engine (like Google, Yahoo, Bing) to rank your website?
It means to start showing your page (from your website) higher and higher within search results. Everybody tries to land their pages in TOP 10 of search results.
Those are also called TOP 10 Rankings, because they are the pages which are ranked the highest in the search result pages.
More in the SEO Wiki
What Is SEO? How Can You SEO a Website?
Why Use Keywords?
In Social Media
Keywords and Topics