From what I understand Alexa will not even recognize your site unless your visitors are using either the Alexa toolbar for IE or the Search Status extension for Firefox. (There may be other toolbars and extensions also, these are just the ones I know about.)
I'm not comfortable with relying on my visitors to have these tools installed. I want to ensure I'm receiving credit for my traffic by every person that visits my site regardless of whether they have the toolbars or extensions installed. To do this I figured that I'd have to put something on my blog to trigger the transmission of data back to Alexa's site.
That's why I installed an Alexa Site Widget on my blog. I don't know if it is a coincidence or not but I went from 4,080,035 to 1,364,067 in just a few days. If my theory is correct then every visitor to my blog downloads the Alexa site widget when they visit my blog and that is how Alexa receives data on every visitor. (not that there are very many visitors here! hehe).
If you want to try it on your site you can get it here. Can't hurt, right?