PageRank specifies the importance of a web page. A Web crawler may use PageRank as one of a number of importance metrics it uses to determine which URL to visit next during a crawl of the web.
PageRank measure's a web page's importance. A Score out of ten assigned by google to each indexed web pages. The visible result of the algorithm, but note that the “public†PR is not the same as the ‘true’ PR and is only updated infrequently. PageRank is one of many factors that determines where your web page appears in search result ranking, but if all other factors are equal, PageRank can have significant impact on your Google rankings.
Yes, you can think that page rank is a mark sheet. Google give the marks out of 10. Google give the marks on the site for their relevancy and good attitude. Some webmaster think that google Page Rank and Page SERPs are the same things but actually not. Their is no reason for good ranking for High Page Rank. That's True.
In addition to what the other posts have said, Google PR gives a pretty accurate representation as to how much a link from that page will be worth. You can rank above a site that has 5000 back links with only a few hundred if your links are from sites that have a PR6-7-8 etc. and their links are from sites with PR1-2 (although how likely any private site is to get a backlink from a PR8 site is questionable.) Having a high Google PR does not directly help your search engine rankings, however if you have a good PR, then links from your site will be worth more, and you can therefore request higher PR links in return. In essence, Google PR is how valuable Google deems your page to be as a source of accurate information, hence why wikipedia's pages all have such high PR, because Google knows that it is a site full of quality information from the amount of quality sites that link to it and the amount of people that go there for their information.