PageRank is the measure of the importance of a page based on the incoming links from other pages. In simple terms, each link to a page on your site from another site adds to your site's PageRank. Not all links are equal: Google works hard to improve the user experience by identifying spam links and other practices that negatively impact search results. The best types of links are those that are given based on the quality of your content.
When a user enters a query, our machines search the index for matching pages and return the results we believe are the most relevant to the user. Relevancy is determined by over 200 factors, one of which is the PageRank for a given page
In order for your site to rank well in search results pages, it's important to make sure that Google can crawl and index your site correctly. Our Webmaster Guidelines outline some best practices that can help you avoid common pitfalls and improve your site's ranking.
Google's Related Searches, Did you mean, and Google Autocomplete features are designed to help users save time by displaying related terms, common misspellings, and popular queries. Like our google.com search results, the keywords used by these features are automatically generated by our web crawlers and search algorithms. We display these predictions only when we think they might save the user time. If a site ranks well for a keyword, it's because we've algorithmically determined that its content is more relevant to the user's query.