Page rank is a simple rating given by google to any page in a website. The scale is upto 10.
If your PR is high, it says google does give lot of importance to your page.
Check statcounter.com. Index page is 10 PR.
Again a high PR comes from backlinks. That too not only number count, PR of the page which has the link also matters. If a 8 PR page contains your link, that weightage of 8 PR is propagated to your website. If you have too many 1 and 0 PR backlinks, the PR contributed to your web page is negligible and consequently your web page will not acquire a good PR.
oogle has its own pagerank algorith which determines the PR of a page from a number of factors like PR of page linking to , number of backlinks, link relevancy etc.
Google PR and backlinks are not live. It gets updated by google once in a while (not overnight). That is called a google update. There comes an increase / decrease in number of backlinks and PR. Usually PR does not guarantee ranking, but surely there is some relationship as both depend upon backlinks.