The PageRank of a given page in a web is a measure of the chance that someone randomly selecting links between pages will find that page. This means that high PageRanks get assigned to pages with many incoming links, especially from pages with high PageRanks themselves.
Several documents describing PageRanks in more detail and the mathematics by which they can be calculated can be found on the WorldWideWeb - a search using Google turned up http://www8.org/w8-papers/2c-search-discover/measuring/measuring.html within the first ten results.
While http://www.google163.net/blog/archives/000333.html is broken, I have found this link at http://www.seochat.com/seo-tools/pagerank-search/ which may be related to the original.
I am curious though, what use can you make from the results of using such a tool? I am not a WebSite designer so please use terms I can understand.
In response to the above question. The page rank is an indication of how Google has been viewing your site for the last 3 or so months, they don't actually display the current page rank for your site, although they do use it internally as part of the calculation for determining where you should rank for a particular keyword. There are other factors that are used to determine exactly how you rank for a keyword - content, the number of time the keyword or related terms are in the page, the metatags, your url, the title of the page, etc, etc. There are many resources out there that can help you to understand this, both online and offline, including an "SEO for Dummies" book that you can pick up at your local bookstore.
See also: BackLinks
PageRank importance and calculation of pagerank is well explained at http://blog.eukhost.com/2006/09/21/description-of-pagerank-calculation/ . There are many other good articles to understand pagerank. Simple search in google should lead you to some good articles. Is this LinkSpam?