No, they're to ensure your site is fully indexed by the search engines. If you aren't indexed then you can't do well in the SERPs but those pages that are indexed can still attain a decent pagerank.
what does that mean? My sites don't have a relationship with any "web" but with search engines - and usually only 1 search engine per sitemap - in this case Google (since the OP posted in that category).
There is no relation between page rank and sitemap. Sitemap is used to help the search engines to find the pages in your site where as page rank reflects the quality of a given web page and is often determined by the number of back links though there exists other on page factors.
Sitemaps are designed to direct or control the search engine spiders on viewing and indexing your site. It can help with rankings if the spiders can not find information and links without the sitemap. Meta tags and page content as well as backlinks are the main areas of page rank.