It's easy to be confused by PageRank (PR) if you're new to SEO -- and even if you're not. To begin with, the rank or position of a page in the Google's free results and the PageRank of a page are two entirely different things. PageRank refers to the Google's idea of the importance of a page, whereas, the rank of a page is where it is found in the Search Engine Results Pages (SERPs) for a given keyword or phrase.
PageRank, in its earliest incarnation was the metric that set Google apart from other search engines. Central to Google when the search engine emerged, PageRank was a calculation based on links (both internal and external) that reflected the likelihood of a random surfer landing on a given page.
It's important to make a distinction between Toolbar PageRank (TBPR) and Actual PR.
Simply put, Tool Bar PageRank was – and still is -- an indication of Google’s estimation of the importance of a page on a scale of 0 to 10, with 10 being more popular. Toolbar PR is the only PR we can actually see.
Actual PR is calculation of a range of 0-1 or if expressed as a percentile 0-100%.
Wikipedia's entry does a good job of explaining PageRank as it was first conceived, the original formula for its calculation and its historic relationship to Google’s algorithm.
Over the years, Google has refined PageRank and changed the algorithm to better reflect the value of a page. From: http://www.google.com/corporate/tech.html (bold is mine):
PageRank Technology: PageRank reflects our view of the importance of web pages by considering more than 500 million variables and 2 billion terms. Pages that we believe are important pages receive a higher PageRank and are more likely to appear at the top of the search results.
PageRank also considers the importance of each page that casts a vote, as votes from some pages are considered to have greater value, thus giving the linked page greater value. We have always taken a pragmatic approach to help improve search quality and create useful products, and our technology uses the collective intelligence of the web to determine a page's importance.
Why is ToolBar Page Rank Called FOOLbar PR? In December of 2000, Google released a browser toolbar that included -- among some other handy tools -- a button that revealed the PageRank for any given page. The ensuing rush to improve PageRank through link exchanges, purchases or other link schemes that focused on PageRank alarmed Google. It was all too easy for webmasters to manipulate their position in the free results.
In order to combat that practice, which Google calls “spamdexing," the search engine stopped releasing current PageRank data to the toolbar. When toolbar PR is updated now, it is generally several months old making it impossible to know the actual PR of a page. Toolbar PR became, at best, an outdated expression of the PR of a page at some point in the past. It became a Fool's Errand to use the toolbar to guess at actual PR. Hence the nickname, FoolBar PR.
How Important Is Page Rank? We don’t know. We know it’s one of 200 or so factors that Google uses to determine where a site should rank in the SERPs. We know that it was the basis for the technology that made Google a household word.
If PageRank Is So Important, Why Do Lower PR Pages Frequently Outrank Pages with Higher PR? First of all, while we do frequently observe pages with lower PR outrank higher pages, since we are using Toolbar PR as our source, and we know it is not a reliable report of a site's current, actual PageRank, we don’t know if that’s an accurate observation at all.
What we do know is that Page A, with an overall PR of 2 might be more relevant for a particular keyword phrase than Site B with PR3. On another keyword search, Site B may rank higher than Site A. The links are important, yes, but the anchor text and context of the links are also important. PageRank is not the whole picture.
It's also relevant to understand that while TBPR is expressed in whole numbers, actual PageRank is calculated on a scale from 0 to 1, with any calculation in between ... so, assuming Google "rounds up" a page with a TBPR of 1 might have any actual PageRank of anywhere from .05 to 1.4999999....
It’s probably safe to say that we do know that actual PageRank is now calculated rather differently that the original formula, and while we don’t know what the algorithm really is, for those who are interested in delving into how Google may calculate PageRank today, an examination of a recent patent award to Google may offer a great deal of insight: http://www.seobythesea.com/?p=3806. The patent suggests Google has changed its calculation of PR to include such things as the location of a link on a page, the size or color of the font, as well as the various aspects of the context and the source. It also explores user behavior that might be collected from a toolbar and its potential impact on PageRank. Serious SEOs will want to study this patent, IMO.
The Anatomy of a Large-Scale Hypertextual Web Search Engine Sergey Brin and Lawrence Page
This 2007 article on PageRank http://searchengineland.com/what-is-...bmasters-11068 may help in understanding the basics of PageRank.
Matt Cutts on PageRank Sculpting: http://www.mattcutts.com/blog/pagerank-sculpting/