PageRank is the first iteration of how Google ranked pages based on inbound links. This is published in Google’s first patent discovery document and is public knowledge and always has been. The PageRank of a page in this iteration is calculated by adding the page rank of every page that links to it (except for links from the page itself) and dividing it by the number of outbound links on that page, reduced by the damping factor, to 1 minus the damping factor.
Google used to publish a representation in a scale of 1-10 known as toolbar PageRank (tbPR) via a browser plugin that should a pipe chart with the scale of PR of a page/domain name and also made it available via an API. This somewhat backfield as people became obsessed with it and it led to a widescale rise in link buying. By the time Google realized this, it was too late – resulting in the suspension of a large number of domains that were targeted by the Google Search Quality team and algorithmic updates. Google subsequently pulled the tbPR broswer plug-in and API – which was also used by SEO tools like WebCEO and Alexa (a former search engine turned SEO tool) which has since been replaced by a public version called Domain Authority,which has been subject to much debate and a lot of skepticism in the SEO community.