hey confused,
welcome to the non confusing world of seo where the waters are always calm and everything is so crystal clear ;-).
The blue "i" button shows a mysterious quantity of links that point to the page you are on. It is a poor metric in my opinion, and the opinion of many for measuring backlinks. In order to check backlinks, I recommend using Yahoo and querying- linkdomain:yourdomain.com
This will show you a more complete picture of who links to your entire domain. And the results tend to be ordered by sites deemed more valuable by Yahoo.
Alexa is a company owned by Amazon. Alexa rankings do not measure links - they measure traffic. Supposedly. Many webmasters find their information highly inaccurate. The lower the Alexa ranking, the more trafficked the site is (supposedly).
Many agree that the metrics in our industry - such as toolbar PageRank, MarketLeap scores, and Alexa rankings are highly inaccurate - but hey, those are the tools have at this point in the game. Love 'em or hate 'em, we are forced to rely on them to some extent. Particullarly when buying links.