What is PageRank?Short Answer : A link based metric meant to represent trust/authority.
PageRank (PR) is a method developed by Google as a way to rank a URL based on the volume of links to that URL, and the trust/authority/popularity of the linking pages.
How can you see PR?Short Answer : Google Toolbar (PR checking services that use the GT PR call).
Technically, you cannot see the real PR.
What you can see is a Public version (which is less detailed/accurate, and updated far less often).
The Public PR score is a figure between 0 and 10, and traditionally only updated 4 times a year (though sometimes G may take longer and thus fewer updates).
The Internal PR score (the one used by Google) is meant to be far more detailed (decimal places etc.) and updated far more frequently.
How does PR work?Short Answer : PR is passed and acquired through Links.
The amount of PR value passed through a link can/does vary, depending on things like PR of the linking page and the number of links on the linking page.
A link from a low PR page will provide the destination with less value than the same link from a high PR page.
A link from a page with a lot of links will pass less value than the same link from a page with fewer links on it.
What affects PageRank?Short Answer : Links.
PR is based on Links, and only Links.
Though there are many other factors around links (such as relevancy etc.), the PR you see is not affected by any such thing.
There are numerous myths about PR - and they are not true (thus why I said myths :D).
Things like "PR leaks through links", or "Links from a .gov domain are worth more" etc. are false/incorrect.
PR is purely a score based on Link Popularity.
Why is PageRank important?Short Answer : It can be one of the more influential Ranking Signals used by Google.
At the end of the day, Links are an important set of signals that G look at. PR is just one part of the Link Signal Set, but G may pay a lot of attention to it, esp. if they have to choose between highly similar content.
(Say you have 2 books about the same subject to read - which would you choose? The one that everyone you know has read and stated was good, or the one no one has read and no one talks about?)
Do all links pass PR?Short Answer : No.
Google introduced a a value called nofollow. This could be applied to the Robot Meta or to specific links (as a micro-format).
The idea behind this was that you could tell Google that some links should not pass value - think of things like adverts or links in comments.
So if G sees a page with nofollow assigned to it, or sees a link with nofollow, then they may not pass PR through the link(s).
(I say "may not" as it is at G's discretion, and they may decide to do so regardless of the nofollow usage.)
So what has this got to do with Google Plus?Short Answer : I'm not quite sure...
More seriously - G+ is an important step for Google on many levels/in many ways.
To the point, they even inject some G+ content into the Search Engine Results Pages (SERPs).
But it appears that G still adheres to it's older/more established patterns of behaviour with G+ content, possibly including deciding which posts to shove into the Search Results.
More importantly, G+ is a social platform that permits interactions and promotional activities.
In short, it's a way that you may get links to your content, (as well as targeted traffic if done right).
Thus understanding the What, Why, Where and How of PageRank is important.
That just leaves you with the need to understand how PR works within Google+.
And this is what the blog is for - looking at how PageRank and Google Plus interact.
Resources.Well, just in case you want to look further into this, these may help;
- Patent : Method for node ranking in a linked database (United States Patent and Trademark Office)
- PageRank (Wikipedia)
- What Is Google PageRank? A Guide For Searchers & Webmasters (Search Engine Land)