PageRank is one of the many ways used by Google to define the relevance or importance of a site.
Google interprets the links from the page A to the page B as a vote of A towards B. Of course not only the amount of votes matters but also the quality of the voting pages.
PageRank is based on the amount of the incoming links but the relevance and the quality also matters.
PageRank(A) = (a-d) + d(PageRank(t1)/C(t1) + … + (PageRank(Tn)/C(tn)).
Not all links affect PageRank equally.
If a page with PageRank 8 has only one link, then the site it takes to will receive the entire PageRank. And if there are 100 links, every of them will get only some part of the PageRank.
Bad incoming links don’t affect PageRank.
PageRank considers the lifetime of the site, the relevance of the incoming links and their lifetime too.
The content doesn’t matter when calculating PageRank.
PageRank is calculated not for the whole site but for every page.
Every incoming link is important but the links from the banned sites.
PageRank is not only the integer value from 0 to 10. It’s a real number.
It’s getting harder to reach every next PageRank level. I guess they use the logarithmic scale.
PageRank is always recalculated but the toolbar data is updated once a few months.
Google tries to find good and relevant pages at the same time.