To be accurate this term is written as "PageRank" because it is trademarked by Google; however, it is commonly seen and written as "page rank." It is Google's ranking software that calculates how relevant a Web page is to the keywords a user enters when doing an online search on Google.com. This software (which operates behind the scenes) analyzes both the number of incoming links and the quality of the referring Web page. It then produces a relative measure between 0 (low) and 10 (high) which is seen as a green bar next to the search result on Google.com (above), or seen as a number in the Google Toolbar on your browser.
As Google explains: "PageRank relies on the uniquely democratic nature of the Web by using its vast link structure as an indicator of an individual page's value." Google interprets a link from page A to page B as a vote, by page A, for page B. But Google looks at more than the sheer volume of votes, or links a page receives; it also analyzes the page that casts the vote. Votes cast by pages that are themselves "important" weigh more heavily and help to make other pages "important."
Enormous amounts of information is available online for those of you trying to figure out how to best take advantage of the page rank algorithm (but unfortunately it is often quite unreliable). Suffice to say that if a Web site with a PR = 0 links to your site, this will NOT negatively afflict your page rank; however, if YOU link to a PR = 0 Web site, you will be penalized (sad but true). For more discussion, check out the links below!
Webmasters: Be sure to click on "more info" below for an excellent article on "How to Understand Page Rank vs. Link Popularity and Linking Tips for Blogs!"