Alexa rank is a relative measure of the popularity of a website based on the amount of traffic to the site. It measures rank based on the amount of traffic from users who have the Alexa toolbar installed and therefore is not a true measure of rank. Mainly because it is restricted to only the population of users (mainly technical users) who have the toolbar installed. It also only measures number of visits and discounts any information about the usability of the site.
The lower the ranking, the more popular the website is. For example, Google.com had an Alexa rank of 1, Yahoo.com had a rank of 3 and Bing.com has a rank of 5 on the day that this article was written. The Alexa rank values are calculated from the number of unique visitors and the number of page views per visitor over a 3 month rolling time period. The site with the highest number of unique visitors and page views ranks number 1 (i.e. www.google.com). This ranking is provided only for the top level domain of the site.
The value of an Alexa rank result is strongly debated, however, it is widely used as a measure of site popularity (i.e. the amount of traffic to the site) and is sometimes used as a measure of potential advertising revenue and therefore this ranking value should not be disregarded.