Larry Page developed a mathematical algorithm for determining the importance of a site based on the links it has received. This research was done at Stanford and licensed to Google who now have the term PageRank trademarked. At the time of introduction in 1998, PageRank was a relatively revolutionary technology which put Google’s search results way out in front of competitors’ in quality.
As this system is not immune to ‘gaming’ by professional SEO firms, the techniques used by Google and other search engines has had to develop to take into account some other measures such as content quality measures brought in with the Panda update.
Whilst knowing the PageRank for your sites is still a useful tool it is of diminishing importance to focus on PageRank as other ranking factors move to prominence. Google has even removed the public PageRank from the Webmaster Tools application and updates to the public PageRank information have become so infrequent as to be unhelpful in measuring an SEO campaign or other web project.