In a nutshell, it considers links to be like votes. In addition, it considers that some votes are more important than others. PageRank is Google's system of counting link votes and determining which pages are most important based on them. These scores are then used along with many other things to determine if a page will rank well in a search.
Danny goes on to say that Google is somewhat qualifying that PageRank is important but not the sole factor in how pages are ranked.
He supports this fact by illustrating with an easy example.
In the above result, you can see that Movies.com which is listed first has a PR8 score while the Internet Movie Database listed second has a PR9. The page with a lower PageRank still got the higher search rank!
Here are some more interesting points at the end of his article.
PageRank tells how important a page is, relatively speaking, compared to other pages.
PageRank is just one of MANY ranking factors used to determine ranking in search results.
High PageRank does NOT guarantee a high search ranking for any particular term. If it did, then PR10 sites like Adobe would always show up for any search you do. They don't.
The anchor text of a link is often far more important than whether it's on a high PageRank page.
If you really want to know what are the most important, relevant pages to get links from, forget PageRank. Think search rank. Search for the words you'd like to rank for. See what pages come up tops in Google. Those are the most important and relevant pages you want to seek links from. That's because Google is explicitly telling you that on the topic you searched for, these are the best.