Google Page Rank is a number from 0 to 10 that Google assigns each page on the internet based on how "powerful" that page is in terms of the number and quality of links coming into the page. CNN is a Page Rank 10, my mom's blog is a 1, this blog is a 6... you get the idea. Because Google reveals this number in their browser toolbar, a number of SEO tools and toolbars started to use it as a relevant metric to evealuate the "Google Juice" of a given website or web page. All of this resulted in a near obsession among most SEOers and many marketers on their own Page Rank. People used to sell links, and charge more for links from a higher Page Rank site. Google started not to like that people were focusing on this metric, and started to delay the data in the toolbar, meaning that there was a 6-9 month (or longer) delay between what Page Rank Google assigned to you and what the publicly available Page Rank was. And there were rumors and suspicions that Google no longer used Page Rank and had moved to Trust Rank, which was not available publicly but was the new version of Page Rank.
Fast forward to today, and I think Google Page Rank is a completely irrelevant metric to track, and here are 5 reasons why.
Metrics are useless unless you can track them, and you can't track Page Rank. The best approximation of your Page Rank you can get is 6-9 months old, and even then you're not sure it is correct. If you cannot accurately and frequently get new data for a metric, it is pretty much useless.
Page Rank has nothing to do with SEO rankings or results. I know of websites that have a Page Rank of 0, and yet they still get organic rankings and search traffic for competitive search terms.
Page Rank is not relevant for real time search and social media results. Increasingly, social media conversations, real time news and status updates and other content are making their way into search results. Even though the Page Rank for a tweet or status update is 0, they still show up in results. Same thing for news releases and other content.
Page Rank is not a results metric. Typically it is best to measure things that get you real results for your business (customers and revenue) or things that directly lead to those metrics (leads). But Page Rank has nothing to do with any results - see the previous two reasons.
Even Google says Page Rank is not important. Google removed Page Rank from its webmaster tools because it is not important. Google Employee (Webmaster Tools Analyst) Susan Moskwa says "We've been telling people for a long time that they shouldn't focus on PageRank so much; many site owners seem to think it's the most important metric for them to track, which is simply not true. We removed it because we felt it was silly to tell people not to think about it, but then to show them the data, implying that they should look at it." And many other places Google tells you to not worry about Page Rank.