This two-part guide will introduce you to page rank and page rank optimization (page rank sculpting) of a website using internal link structure. In the first part of this article we’ll explain what page rank is, how it works and how it’s distributed, while the second portion of the article will focus on page rank sculpting.
Google and Page Rank
Page rank was invented by Google's co-founder Larry Page (hence the name Page Rank) as a way of determining the importance of web pages. At the time page rank was invented, search engines relied on text analysis, meta tags and on-page criteria, all of which were easy to manipulate. Early search engine optimization companies employed coders who reverse-engineered algorithms in order to produce high-ranking pages at will. Page rank made it possible to calculate the importance of each separate page on the web, rendering many on-site SEO techniques useless.
For more information on page rank check the following sources:
http://infolab.stanford.edu/~backrub/google.html
http://en.wikipedia.org/wiki/PageRank
Relevancy vs Importance
It's important to understand that page rank does not compute relevancy, only the importance of each page. When a user makes a search query, a different algorithm calculates the relevancy of page, while page rank simply selects the most important result.
User enters the search query.
Google selects results that contain the search term (aka keyword).
Selected results are sorted by page rank from the most important to least important results,
Results are displayed to the end user.
Different algorithms are responsible for relevancy calculations. From an SEO perspective, keywords in anchor text, title tags and content are some indicators of relevancy.
Search Optimization 
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