Let´s first start by defining this phrase: Google Page Rank(PR):
Google simply counts the links that point to a site and increases or decreases its Page Rank depending on the number and the quality of these links.
The essential idea of Page Rank is: a reputation, as your website has a good reputation so it wins higher Page Rank, and as it has bad reputation so it loses Page Rank, so easy!
But who decides what is your site reputation?
The answer is: The Back Links.
So the more backlinks your site has, the better Page Rank will be awarded from Google, and vice versa.
It is like a human society: when more people say that you are good so your reputation becomes better.
On the other hand the quality of these backlinks plays a big role in deciding the effect of these links, e.g: if your site has one backlink from another website which has PR=6 so it will be more benefit than getting10 back links from websites which their PR=3 or less.
How to improve your site´s Page Rank?
The relation between backlinks quality and google Page Rank is steady and the answer of this question leads us to reply the correspondent question:
How to improve your site´s Backlinks?
To get the max influence from your site´s backlinks you should be attention to these points:
1. Backlinks quanity:
The more number of backlinks your website has from unique sites the better Page Rank it gets, it is like an elections in real life, more votes leads to better rank in the list.
2. Quality of backlinks resources:
When the backlink comes from high Page Rank website it will affect positively much more than when it comes from low Page Rank website, so it is not just a quantity issue rather than quality subject.
So instead of wasting time of getting lot of links from sites with 1 or 2 Page Rank you can get the same reputation if your site has few backlinks from 7 or higher Page Rank.
3. Age of backlinks:
Some backlinks may stay for short time in its place (days or weeks)then it goes away, others stay for long time (months or years).
Google has smart tools which consider that backlinks with a long life are as an indication of credibility so better Page Rank will be given for the connected website.
4. Generous websites:
Google observes the origins of your website backlinks, it counts the quantity of links that these websites generate, if one website was so generous and tries to help lots of another websites by giving them links so the influence of these links will decrease according to the quantity of these backlinks (if the number was so big then the influence will be zero).
So try to get your links from a site that gives minimum quantity of them.
Is Google Page Rank is so important in SEO?
Although Page Rank is an important factor when you work on improving your website´s SEO but it is not the only one.
Google consider about 200 factors when evaluating any website (you can learn some of these factors in my article: Increasing Website Traffic), so it´s a complicated picture when we talk about SEO and Page Rank is just a part of it.
There is no doubt that Page Rank leads to better results in SERPs (search Engine Result Pages)and also it attracts more links from other sites as they will be willing to get backlinks from your site which will give them better PR, and this will leads also for more traffic for your site.
But as said: Page Rank is not the only player and it is not recommended that you spend most of your time focusing on this point and neglect the other factors as you may see some websites of lower Page Rank defeat sites with higher Page Rank (but have worse SEO factors).