Google Page Rank are logarithmic value given to each web page based on its importance. The importance is determined by the number of citation(links) that a page receives both internally(from the same website) and externally(from Authoritative and New Websites). Earlier page rank was defined simplistically
What is Google PageRank?
As you can see, a web page with a page rank 100 divides its value equally with two linked pages But this led to a situation where if pages are linked in such a way that it goes into an infinite loop(like below) then all the pages will have a page rank of 100.
To avoid this, Larry Page introduced a concept called 'Damping factor', which dissipates 15% Page Rank value with each link. The page rank is based on random surfer model, which states that even for random visitors browsing through pages, with each click the probability to click another link is at 0.85 (losing 15% of page rank value with each click)
Google Page Rank(Definition By Google): 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.
Random Surfer Model has become unreliable, especially because of the assumption in the model. The assumption was that users randomly surfs the web pages after reaching a website. But as real users, we know that each of our search has an intention, either to assimilate information, find an answer or to formulate an opinion.
Intentional surfer model explained page rank in a much better way. This model considers user intent while evaluating the importance of each page. This is mainly calculated using Google Toolbar(if you have installed in your browser), which sends information about browsing patterns, thus indicating the importance of each page.
The navigational elements in your website plays a big role in guiding the users to different pages and thus contributing to the importance of each web page. Links from within the body of the text has more value than navigational elements in sidebars or footers.By providing related links and linking to related pages within the text, you are encouraging users to browse through other pages. More actions(page visits) the users perform per visit, more valuable will be your website for that 'Search Term'.
It is important to link to pages that have the same theme, for easy accessibility and also for better user experience. Remember, Google's mission with Search Engines is to make the user's search experience enjoyable. If each visit to your website is contributing to the positive user experience for Google Search Engine, your webpage will be more valuable to Google.
However, better linking in itself will not help your webpage to rank number one for a particular search term.This is because Google takes into consideration more than 200 signals including citation(links) from authoritative sites, Anchor Text in the Link, Popularity in Social Media and the Age of the site. The Algorithm is updated every week.