PageRank is a system for ranking web pages. PageRank is the name of Google’s link authority algorithm. The higher the PageRank of a link, the more authoritative it is.
PageRank is an intricate algorithm that gives a score to a webpage based on its importance. It gives the score on the scale of 0 to 10 that is shown on the PageRank toolbar. A great article that explains how PageRank moves is over at SEJ here. PageRank gives a good understanding on how to execute SEO strategies. Content is still king and generating high quality links is crucial in getting high scores.