PR is googles ranking system.
Tools like this check against the google data centers:
http://www.mygooglepagerank.com/
To put it simply, the more backward links a page has the higher the PR. According to google, the higher the PR the more SE traffic.
BUT, as many will attest, PR really isn't the end-all-be-all. It's actually a pretty poor measure of a site's/page's value, but it's easy, so a lot of people use it when considering link trades because it requires less thinking.
