The  algorithm that Google uses to assign a weighting to each element of a linked set of documents, with the purpose of "measuring" its relative importance within the set. 
A particular websites PageRank results from a "vote" from other pages on the Internet about how important that website actually is. A link to a page is seen as a vote of support. The PageRank depends on the PageRank rating and number of all pages that have links to it. Additionally, if a page is linked to by pages with a high PageRank rating, this increases the rating of the original page.
The PageRank scale ranges from 0-10. The rating of a certain page is generally based upon the quantity of inbound links as well as the perceived quality of the pages providing the links. 
PageRank could be described as a probability distribution representing the chance that someone randomly clicking on links will reach a certain page. The PageRank calculations require iterations through the collection of web pages to alter approximate PageRank values to accurately reflect the actual rank.
In order to prevent spamming, Google releases little information on the way in which a PageRank is calculated. The PageRank algorithm has led to many sites being spammed with links in an attempt to artificially inflate the PageRank of the linked page, notably in blog comments and message boards. In 2005 a ‘nofollow’ tag was added as an attribute of a HTML link to be used where Google shouldn’t change the PageRank of the linked page as a result of the link.