I don't understand what the page rank is. Can you explain? The way I imagine it is you get a different page rank as the result of a different query -- so if it's done right I would merit a higher PR for someone searching "Scheherazade Stay of Execution" than for someone searching "Britney Spears Esq. pics". More info, please....

Right, I think that Steve, my favorite Google consultant (his blog is here), would be better to ask, but here's my understanding: Google works mainly through analysing link patterns: a page is considered more authorative for a subject depending upon the links from other pages that link to it. It also makes a difference what kind of link it is: if I link to your site with the words bankruptcy lawyer, it bumps your site up more in the rankings for the term 'bankruptcy lawyer' than if I link via your name but mention the term several times on my site. (This is why I keep linking to Steve with the term "Google Consultant": I'd like him to own the term. And my analysis below explains why I'm not doing it here.) Your page's pagerank is a measure of the authority that Google gives to the referring page with reference to the referrer. So for instance, it considered my links to you more important when I had a PR6 than when I had a PR5. Search engine optimisation specialists like sites with a high page rank, because they're useful for manipulating Google. Suppose I have a product (a PDA, for instance) whose site I want top-ranked for the term 'PDA.' I might send a free unit to several influential blogs/sites/etc. asking for a link to the product with 'PDA' in the link. Your authority is determined by a lot of things, including how many people link to you. Now, here's why I think that Google's PR calculations now give links in comments negative weighting. From what I can tell, your site, my site, and AI's get similar amounts of traffic, certainly within orders of magnitude. Your entry in Technorati isn't appreciably better than mine or AI's. However, he and I are frequent commentators on other blogs, to a degree you're not. Each of those comments will leave a link back to our sites in the comment field. I think these are now being counted against us--hence your remaining at PR6, and our drop. (We all rose to PR6 in the update before last, if I recall correctly.) Now, why might Google do this? I can think of one very good reason: it radically discourages comment spam. After all, if by spamming blogs you're only hurting your own standing, there's an awful lot less point in doing it. All this is guesswork, although I'm working on some empirical testing. I'm authoring all my comments in other blogs with an alternative URL that uses .htaccess to forward the user to my real website. If I'm correct (and Google hasn't compensated for this tactic), I'll start rising back towards PR6 in the next update. I'm using AI for a control in this admittedly unscientific experiment.

You've got it mostly right Tony, except your points about things 'counting against' you and about the linking copy (the anchor text). From both my experience and from the explicit statements from Google representatives, such adjustments by Google to reduce the over-influence of high PR blogs, will never count against you, they will simply not count for you. It has been this way with forum posts for some time. Google no longer considers the links on forum posts as relevant, so regardless of your attempts to spam them, Google will ignore you and significantly won't actually penalise you. Anchor text itself does not contribute directly to PageRank. PageRank is exclusively about the pattern of link relationships between sites and their relative weighting. You will notice also that when checking a site's inbound links on Google, using the Link operator in a search, only those sites with a PR4 tend to show. (I use Alexa.com to get a broader picture of inbound links). Generally the notion of an 'authority' site is more conceptual than defined and empirical. Basically you have to have a good PR for your sector, lower reciprocity in your linking and good relevance of the anchor text to the site content, but beyond that you either know it or you don't. The over-influence of blog trackbacks appears to be being tackled separately as we no longer get empty trackback pages winning fairly high profile searches (The Register reported on this last October). Hope that helps.

Good advice. My blog is http://zombielogic.myblogsite.com/blog