PageRank is a algorithm used by Google to measure the relative importance of web pages, and it was publicly shown in the Google toolbar and other browser addons, until Google stopped updating it. See also: How often is pagerank updated?
The PageRank that is publicly known was heavily based on links, which made it particularly vulnerable to the manipulation of website owners. Entire directories existed just with the purpose of providing free links for our websites, these would quickly loose their influence when Google started ignorering such links.
Typically pages with a higher PR, would also be positioned higher in the search results.