I was wondering if the page rank and the backlinks are just for one page?
From a great article done in 2007 by Smashing Magazine on PageRank, I draw your attention to #2, #3, and #9 in relation to your first question (i've included their other points for educational purposes):
- PageRank is only one of numerous methods Google uses to determine
page’s relevance or importance.
- Google interprets a link from page A to page B as a vote, by page
for page B. Google looks not only at the sheer volume of votes;
among 100 other aspects it also analyzes the page that casts the
vote. However, these aspects don’t count, when PageRank is
- PageRank is based on incoming links, but not just on the number of
them – relevance and quality are important (in terms of the
of sites, which link to a given site). PR(A) = (1-d) +
d(PR(t1)/C(t1) + … + PR(tn)/C(tn)). That’s the equation that
calculates a page’s PageRank.
- Not all links weight the same when it comes to PR.
- If you had a web page with a PR8 and had 1 link on it, the site
linked to would get a fair amount of PR value. But, if you had 100
links on that page, each individual link would only get a fraction
of the value.
- Bad incoming links don’t have impact on Page Rank.
- Ranking popularity considers site age, backlink relevancy and
backlink duration. PageRank doesn’t.
- Content is not taken into account when PageRank is calculated.
- PageRank does not rank web sites as a whole, but is determined for
each page individually.
- Each inbound link is important to the overall total. Except
sites, which don’t count.
- PageRank values don’t range from 0 to 10. PageRank is a
- Each Page Rank level is progressively harder to reach. PageRank
believed to be calculated on a logarithmic scale.
- Google calculates pages PRs permanently, but we see the update
every few months (Google Toolbar).
From Google's own PageRank algorithm:
PageRank does not rank web sites as a whole, but is determined for
each page individually. Further, the PageRank of page A is recursively
defined by the PageRanks of those pages which link to page A. - The
Page Rank algorithm
The second part of your question was:
should we optimize each and every page of the site and try to bring backlinks to each of them?
To answer this question you need to understand that not only do external back-links create PageRank, but internal links can distribute PageRank as well, so technically you don't need an external back-link to a particular page, but a page of your own with high PR can pass on PR to your own internal page.
That being said - each page should be optimized of it's own accord - written with unique title and content, and in such a way that the page itself would attract it's own back-links. Not only will those back-links help that particular page, but the PR that comes with the back-link will be distributed internally to help other pages in your site that haven't been linked to externally.
In case all this information about PageRank starts people thinking that it's more important than it really is - please understand that PageRank (in of itself) is only one of hundreds of ranking factors, and more recently, has become less of a significant one.