What is pagerank?

PageRank is a link analysis algorithm used by the Google Internet search engine that assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
Source: Wikipedia.Org

PageRank Technology: PageRank reflects our view of the importance of web pages by considering more than 500 million variables and 2 billion terms. Pages that we believe are important pages receive a higher PageRank and are more likely to appear at the top of the search results.
PageRank also considers the importance of each page that casts a vote, as votes from some pages are considered to have greater value, thus giving the linked page greater value. We have always taken a pragmatic approach to help improve search quality and create useful products, and our technology uses the collective intelligence of the web to determine a page's importance.
Source: Google.Com

The best source to understand and learn things about pagerank I found is this website.

What can we discuss in this thread?
A lot of things can be discussed in this thread, when there should be a new PR update, when the pagerank updated, how important it is to have backlinks with a high Pagerank and so on!

Terms that might be used in this thread (for newbies):
SEO: Search Engine Optimization
PR: Pagerank

Have fun reading this thread, I hope some valuable info will be posted that might help other people!