How Does Page Rank Work?

Pagerank is just one factor of more than 100 that determines rankings for a site and the exact answer to why one site ranks better than another is a closely guarded secret.

lol.. closely guarded secret.

Is it possible that when a website owner buys an expired domain or a second hand domain having high PR ranking this happens? I mean when the first owner was ranking the site for one keyword and generated the site high PR and then the second owner is ranking the site for another keyword. And when you search google for the second keyword the site ends up a few pages back rather than ending in the first page when looking up the first keyword. Would that be possible?

I have a page on a site that jumped to PR3 almost overnight. I didn't have back links, or even good SEO. I began monitoring what was happening, and I discovered that people were finding my page via a search term. That was how they were determining my PR. My page was on Google's page 3 for that search term.

First, you need to understand that it is not a "WEB page rank," it is a "LARRY Page rank" - because Larry Page invented it.

Second, the PageRank algorithm is patented and therefore publicly documented and available as U.S. Patent 6,285,999.

Third, a "simplified" description of PageRank is available on Wikipedia:

PageRank - Wikipedia, the free encyclopedia

Finally, a basic explanation of PageRank goes like this.

"If you just sat down and clicked links at random on web pages, how likely are you to see this one?"

(The mathematicians and probability jockeys will complain about a bunch of stuff, which they can address by going to the Wikipedia article, and if they still have problems they can go read the patent, and if they're still not satisfied they can go write a letter to Larry Page at Google.)

What's important to remember is that PageRank, in the grand scheme of things, is only valuable in a world where nobody knows what PageRank is and how it works. Once people know that there IS a PageRank, and desire their PageRank to be higher, it rapidly becomes useless because the system is easily manipulated.

PageRank has been essentially broken for about a decade, and they just keep patching it to help it limp along a little more... but with each patch, it becomes less useful and less important. Eventually, its value will converge on zero and it will drop out of the ranking algorithms altogether.

PageRank is basically used to break ties. When five results are equally relevant to a given search query, they're placed in descending order of PageRank. Results which are more relevant still go higher in the SERPs, even if their PageRank is not as good.

PageRank is just a way of ranking in numbers how important a page is on the web.
The way to get to the top of google pr is to do things like put the site in your signature link ( although you probably want to use anchor text instead of your URL ), submit it to directories, and so on, and this will help a little bit, but only get you so far.