Alexa's tool bar is used by a lot of internet surfers. With that tool bar installed, Alexa tracks the sites that the users frequent. Alexa uses that data as a barometer to estimate the traffic or importance of a site.
The more important, the higher Alexa rates the site vs others.
The Alexa Rank tool, if this is the same definition you speak of, allows you to load proxies and it simulates Alexa Tool bar users. By loading proxies into the app (it is a php app), it acts as Alexa Tool bar users visiting your site.
The php app reports the clicks (i.e. the http requests to your site via the proxies you load) to Alexa, who in turn sees these "visitors" to your site, thereby increasing your site rank on Alexa ONLY.
I used to have one of those apps, but Alexa has change the url and the algo's that receives this visitor data.
If you know php and want to fool with the old app I used to use, I may be able to find the old app and send it to you. Or, if the other poster confirms that his $30.00 app is what I just described and if it works with the new Alexa algo, then there you are.
It used to work ok till Alexa busted it and changed the algo ( that always happens with BH stuff after a while if too much of it gets out on the market). It may work now as well. I just don't know.