Page Rank, is a number assigned by Google which represents to relative importance of a web page.
The PR for a web page can vary between 0 and 10.
PR is assigned to individual web pages, not to web sites. In other words, it is Page Rank, not Site Rank.
A higher PR number will help you to score better in your SERPS, which will bring more visitors to your web page.
PR is calculated using a complex secret formula which seems to be under constant change.
In general, the more web pages that link to your web page, the higher the PR of your page will be.
Other factors which affect the PR of your web page include the PR of the pages which link to your page and the number of links on the pages which link to your page. A link from a PR7 page is worth more than a link from a PR6 page. A link from a PR5 page with two outbound links is worth more than a link from a PR5 page with six outbound links.
No one outside of a small group of Google employees really understands the Google PR algorithm. Others who claim to fully understand the current incarnation of the PR algorithm are either deluding themselves or attempting to fool you.
Page Rank was original described by Sergey Brin and Lawrence Page in The Anatomy of a Large-Scale Hypertextual Web Search Engine.
A useful and readable explanation of Page Rank can be found in A Survey of Google’s Page Rank.
Brin and Page’s original Page Rank algorithm is attractively described and demonstrated at Page Rank Explained with Bright Colors.
Google Directory Page Rank
The Google Directory uses a different formula for displaying page rank.
Instead of the familiar 0-10 system used by the Google Toolbar, the Google Directory uses a ranking from 0-7.
Google Directory Page Rank is difficult to work with, because no numbers are displayed. All you get is a green and grey bar. An excellent article on interpreting that bar is The Handy Dandy Google Page Rank Figurin’ Guide.