All other things being equal, the page with the highest Page Rank for a search term or phrase will be the first page displayed in Google Search results.
Here is Google's explanation from their own web site...
-  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.
 
 
-  Hypertext-Matching Analysis: Our search engine also analyzes  page content. However, instead of simply scanning for page-based text (which can  be manipulated by site publishers through meta-tags), our technology analyzes  the full content of a page and factors in fonts, subdivisions and the precise  location of each word. We also analyze the content of neighboring web pages to  ensure the results returned are the most relevant to a user's  query.
 
You can find you page rank by adding the Google Toolbar to your browser. This will also show you the page rank of every web page you are on as you are on that page.
For those who do not what to add a toolbar, there are sites such as PRChecker.info that will tell you any pages page rank.
 
you discussed it quite well.
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