Contrary to belief PageRank does not refer to the web page it is named after Larry Page the co-founder of Google Inc. along with Sergey Brin.
PageRank is analysis of links pointing to a website the value is derived from the weight of set of documents that contain the link. It is a complex algorithm which contains many other factors as well. The links on the WWW pointing to a webpage are seen as votes for that page. Hence if a link from page A points to a page B it is passing a vote to it. But the whole webgraph comes into the picture when according a rank.
The PageRank metrics of all pages that link to a webpage are taken into consideration. The pages are ranked from 0 to 10 of which the highest rank 10 is assigned to the most authoritative site. It is believed that page rank does not influence the position on the SERPs since ranking on SERPs depends upon the response to the query. What that means that how relevant is the webpage for the query.
The rank is how Google looks at the webpage or website. It is also a value system on the WWW especially for those seeking backlinks and those interested in a link exchange scheme. To the average visitor this ranking system is unknown but for some it creates trust and authority. The actual ranking system has not been disclosed.
The PageRank is subject to manipulation this can happen by participating in dubious link schemes and paid text links. Being a trade secret it is difficult to know how the leading search company determines to penalize as website.
The rank as shown by the Google Toolbar is only a rough guide to what the search company actually has determined. Google updates the rank of the website only few times a year. For greater information read the Google Web Master Central Blog. One of the blog entry advises web master not to look at this ranking system as sole mertic for the success of a website.
In short this system is just one of the factors in rankings on SERPs. One need not be much concerned with it. I use this system more as a yardstick in order to create a more authoritative website. What matters on the search side is relevance.