Google was founded on mathematical equation of how many web pages are linking to any other web page on the internet. The value calculated by this equation is known as PageRank, named after Larry Page, one of the founders of Google.
For many years the ranking of your website was clearly measured by the number of pages linking to you, but also the PageRank of those pages linking. PageRank is measured on a scale of Zero to Ten, 0 given to brand new web pages and 10 given only to pages that have billions of links. Everyone starts out at a PageRank of 0, but only a handful of web pages every reach the 9 or 10 level.
Up until about 2011, the PageRank of your website was used as a major ranking factor in the Google search results. You would have higher ranking if other sites with high PageRank linked to you. As of this writing, many SEO companies that engage in black hat tactics still tout the importance of Google's PageRank.
Sometime in 2011, Google started to rethink their approach to web spam and link building; at that point they stopped talking about PageRank in their seminars and training videos. It was at this point when PageRank turned into a minor ranking factor for website.
Soon after Google stopped mentioning it most search engine optimization professionals also stopped mentioning it. Looking over my own graph of Daily Golden Nuggets I see that in 2012 I also only mentioned PageRank in a historical context. Although Google never says exactly what's important and what not important for high organic ranking, you can get a good understanding of how SEO works simply by paying attention to what they talk about, and what they don't talk about.
I'm bringing the topic of PageRank up today because it was mentioned in a recent GoogleWebmasterHelp video. I've included the video below. In the video Matt Cutts explains that the usefulness of PageRank is fading but people still like to look at the number.
My bottom line Nugget for today is to tell you that you need to be wary of search engine optimization professionals that sell you SEO services based on increasing your PageRank, and getting you links from website with high PageRank. Those SEO firms are either scamming you or they are not keeping up on new trends.
Either way, chasing after PageRank for your website is a SEO practice that should be considered "archaic" in the internet timeline.