Correct. Page Rank is a kind of popularity contest that has gone bad. Google's original concept was that any site that attracted many links from other sites was "popular", meaning that visitors from the linking sites would be more likely to visit the second (linked to) sites. However, we, as site owners, have screwed up the concept by creating link pages and link farms with reciprocal links that have nothing to do with popularity. Therefore, PR is more a measure of the amount of work to get reciprocal links than popularily, traffic, SERP, or any other measure. In other words, it's pretty meaningless.
What a great quote The example you gave of your new site is very interesting.. What was the topic of the site? I have found there seems to be an 'average PR' for particular topics that you can achieve without much effort. On some topics this is PR4. On others it's PR1/2
Maybe I'm the only one, but my SERPS have always changed quite drastically around the time of any visible PR update (when PR actually went up). So to me, it's more than a "webmaster contest". Just my two cents worth
That is the correct answer for what Page Rank is. It is basically a measure of the importance of a page in the eyes of Google. Like maldives said, it determines how frequently a page is going to be crawled by the googlebot.