PageRank (PR) is one of the most, if not the most, talked about topics when it comes to SEO. Ever since Google released its little green bar a few years ago the whole search engine community has been infatuated with it.
PageRank in short is a way Google measures the importance of a single web page by measuring the number of inbound links pointing to a page, and the number of outbound links pointing out. The idea is that by judging the whole linking pattern of the Internet, more important and higher quality sites will receive more links. It is also known that higher quality web sites also link out to other high quality sites. PageRank is basically Google's way of allowing Internet users to control the results on their search engine.
Although fairly simple mathematically, the logic and purpose behind PageRank is brilliant and the system has turned out to be a very accurate method for ranking web pages.
Many SEO's focus heavily on PR because of the weight Google gives to inbound links. PR is usually a fairly tangible indicator that a lot of webmasters hang onto as it will give you a rough idea of where you stand.
PageRank is thought to be less important these days as the actual theme and quality of backlinks supposedly holds much greater weight in terms of relevancy.