What is PageRank?
PageRank is a numeric value that represents how important a page is on the web. Google figures that if one webpage links to another webpage, it is voting for that webpage. The more links that point to a webpage, the more important that webpage must be. Also, the importance of the page that is linking determines how important the vote itself is. Google calculates a page's importance from the votes cast for it. How important each vote is is taken into account when a page's PageRank is calculated.
PageRank is Google's way of deciding a page's importance. It matters because it is one of the factors that determines a page's ranking in the search results. It isn't the only factor that Google uses to rank pages, but it is an important one.