Page rank is used to assess the importance of a page on the web. It's a value from 1-10 with 10 being the stuff dreams are made of and 1 being Ted's site on geocities :)
Page rank is caluculated by counting links from other sites to your site. It also takes in to acount the pagerank of the page that casts the vote, so a vote from a pr6 will have more influince that a link from a site with a PR of 3 .Google also takes into acount the content of the page that links to you.. so if you where running a site about cars and you got 2 links from pages both with pr5. If one of the links came from a another car site and the other link came from a health site the car link will carry more weight. That is why most webmasters try and get links that are on topic :)
The toolbar is something you need to download from google.com It is an addon to your browser and displays the PR as a green bar at the top. When you mouse over the green bar it will tell you a value.