I often come across this basic question about the difference between
PR and Alexa. Actually it's not that hard to understand.
PR basically is determined by how many quality in bound links is pointing to your site. It is a standard develop by Google and it's used as a ranking to determine how important your site is according to Google search engine.
Alexa on the other hand is determined by the amount of traffic you are getting to your site. The lower the ranking, the better your position.