Tell me what is your PR, and I will tell you where you are. (old saying, a bit rephrased)
The concept of PageRank (or PR) was developed at Stanford University, implemented by Google and now this way or another is used by majority of search engines. PR varies from 1 to 10 (no fractions) and by definition is a measure of an importance of a web page.
The purpose of a search engine is to give to its customer the most relevant search results. Here comes the utility of PR, an optimization on site quality, so the best sites will be offered on top of search results. High link popularity of a site is clearly a merit and PR is its measure. In general, the more inbound links are coming to the page and the higher PR of the source pages, the higher will be PR of this given page.
Consider the following example. Home page of Site 1 has PR 4 and 40 outbound links, of which one leads to your index page. While home page of Site 2 has PR 3 and 3 out-links, of which one points at your site home page. Which site passes to your home page higher PR? Site 2, because in spite of a lower rank, PR of this site is divided by only three links, and hence more PR will be given to your site from this link.
Index page usually gets the highest PR at the site, because as a rule it receives a majority of inbound links. If the site contains some high-visited pages aside from its index, then PR of such pages can be the same or even higher than index page. However, this will be an exception.
You can determine PR for any pages using Google Toolbar in a browser, or through service sites, of which I would recommend My Google PageRank com (I have no affiliation with them, just a neat site:). Of course, the higher PR of your page, the higher probability that it will be listed on top of search results. Here are some examples of high-PR sites: Wikipedia PR 9, Amazon PR 9, eBay Sitemap PR 7, Google Home got PR 8.
PR is just one of multiple factors used in search algorithms. From my own experience, a well-specialized site with PR 4 already can hold steadily number one position on all major keywords in Google and Yahoo searches. If your home page got a modest PR 0-2, dont sweat. It is just a stimulus for further improvement of your site. Writing and posting articles in ezines and blogs, building high quality content on your site and growing number of inbound links from other sites of the same specialization is the best thing that you can do to improve your pages PR.
So good luck, I wish you 10!
Tags: internet, link popularity, optimization algorithms, page ranking, PageRank, PR, Public Relations, search engine optimization, Search Engines, web