What is Alexa Ranking?

I just want to ask about Alexa Rank.
What is the criteria of Alexa Ranking?
What are the benefits of good Alexa Ranking for websites?

Alexa is ranking to your website with others websites all over the web based on number of users and page views.

Alexa is on of the best site of tracking our web site keywords and show to us in which position our site ,,,

Alexa rank is showing that how much site is important for Alexa.com. Alexa rank is same as Google page rank but difference is that showing in important in vice verse way. Means if PR is high in Google it means that much site is important for them and Alexa if number is low then it is most important for Alexa.com.

Hi guys,
I have kind of a similar question. I have a few websites and in my experience, Alexa is very inaccurate. I use Google Analytics to monitor the traffic to my site. I have noticed that when my website is new and not getting much traffic, the Alexa is about 500K. But when the website starts aging and getting some traffic, the Alexa number increases to like 2 million?
Isn't lower Alexa = more traffic?
This doesn't make sense. Who is Alexa? How do they come up with these numbers?

The main Alexa traffic rank is based on a value derived from these two quantities averaged over time (so that the rank of a site reflects both the number of users who visit that site as well as the number of pages on the site viewed by those users). The three-month change is determined by comparing the site’s current rank with its rank from three months ago.

Alexa Traffic Rank is a rough measure of a website's popularity, compared with all the others out there on the internet, taking into account both the number of visitors and the number of pages viewed on each visit.
A site’s ranking is based on a combined measure of Unique Visitors and Pageviews. Unique Visitors are determined by the number of unique Alexa users who visit a site on a given day. Pageviews are the total number of Alexa user URL requests for a site. However, multiple requests for the same URL on the same day by the same user are counted as a single Pageview.
Alexa rankings improves a website’s exposure.