Google see the link popularity of website before giving away page rank to any website. Backlinks increase the link popularity of website and result in getting good page rank as well as position on search engine results.
Google counts backlinks both to the domain and the page. Typically a site will have many more links to the domain but it is not necessarily the case all the time. Each page on a site will have a specific PR and will often times vary PR from the domain. Google judges each page separately and gives them a PR accordingly.