To follow up on Aspen's wonderful entry named PageRank Doesn't Matter?, where he accurately says, it matters, I would like to talk about what Search PR is to most people. If your not in the search marketing field and someone says "how is your PR" you are not running to your browser to check your Google PageRank. You are however, discussing your current public relations efforts to earn visibility for your company in non-direct means.
I am by no means a public relations expert, but I would think public relations ranges from sponsoring a non-profit event to being busted in a insiders trading scheme. All of these 'public relations' gets your name out there for better or worse.
Ok, so now how does public relations work in terms of search marketing? In my opinion, public relations in search marketing can be have a very powerful ripple affect. Let me give you a real example and then we can see if it pans out. Yesterday, this site was linked to from the famous Slashdot Web site. The article can be found here, and you will see this little word that says "writes" is a link to this site. Traffic skyrocketed, take a look:
Most of that traffic was from the Slashdot article, but many other sites also linked to this site based on the Slashdot article. I am not certain, but I strongly believe that the reason Slashdot linked to this site was because of a Google search. This site ranks well for a wide rang of "gmail" related keywords. A simple search brought the author here, which earned a link from Slashdot to this site. Then the ripple affect of having so many readers with content sites of their own also finding this site, then publishing their own articles with a link here and to Slashdot.
The free PR (public relations) from slashdot was (IMO) derived from a search, which will impact further searches (that is where that other PR comes in).
I hope this reads well, I am a bit distracted today. :)