PageRank is a family of algorithms for assigning numerical weightings to hyperlinked documents (or web pages) indexed by a search engine. Its properties are much discussed by search engine optimization (SEO) experts. The PageRank system is used by the popular search engine Google to help determine a page's relevance or importance. It was developed by Google's founders Larry Page and Sergey Brin while at Stanford University in 1998

PageRank is a numeric value that represents how important a page is on the web. Google figures that when one page links to another page, it is effectively casting a vote for the other page. The more votes that are cast for a page, the more important the page must be. Also, the importance of the page that is casting the vote 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.
You can read more about Google PageRank here