Alexa Rank has become synonymous to THE ranking of websites on the internet. This ranking is a direct indicator of it's popularity. It estimates the average daily unique visitors to a website. The estimate is made from the data that is tracked through one of it's browser extensions. Alexa Internet is the company behind this ranking and it is wholly owned by Amazon. Google also has it's own ranking system based on Google Analytics. It is seen that the rankings of the same site can vary quite a bit between these 2 rankings. One reason could be that not everyone uses an Alexa browser extension. This indicates that the sample population is much smaller. However, Google uses a much more broader data source, it's search engine and browser.
Websites are becoming home to people's work and lives. As more an more personal websites and blogs surface, maybe Alexa could be the ultimate indicator of social status in the internet. But the scale of the internet dilutes this to a certain extend where this does not provide much significance to website owners. However, the ranking of a website on a search result page has become more of an indicator to popularity for personal and niche websites.