Page Rank is Google's measure, on a scale of 0-10, of how important (or popular) a web page is on the web. In essence, every link that comes to a web page gets interpreted. Google looks at more than the sheer volume of links a page receives; it also analyzes all the pages that link to it. Links from pages that carry a high page rank weigh more heavily and help to make other pages more "important" than links from pages with a low page rank.
Google views the relationship of the two linked pages as one casting a vote for the other. The more votes a page gets from qualified voters, the higher the page rank for both of the pages being links. Votes are counted as support for web pages, no votes no support.
Of course, pages with a high page rank will not automatically get ranked on the search engines if there is no significant content on the page to match a search query. Google combines PageRank with sophisticated text-matching techniques to find pages that are both important (popular) and contain relevant content to the search query. Google examines all aspects of a page's content (and the content of the pages linking to it) to determine if it's a good match to a search query.