Alexa Ranking -
Basically alexa has a toolbar which 'some' people download and use. Alexa takes information about what websites these users visit and ranks sites based on their popularity. For example - you can check any site. Here is Yahoo which they report as #1 = Alexa Yahoo Ranking
. This data is fairly accurate for sites between 1 and 5k or 10k but after that it isn't. Additionally the rankings can and are easily manipulated or skewed based on other things. Typically not something to worry about much really.
Google Links, MSN Links, Yahoo Links
What this is referring to is the search engines count of the number of backlinks going to your site. (1 = a link from another website TO your website) For example, if you search google for
now for another example check yahoo.com
One note with google's backlink search, and this is important. Google only show's you a sample of backlinks to your site. Only a portion, never the complete universe of backlinks to a site. They do this purposely. So, most seo's will monitor backlinks using yahoo and/or msn to gauge links from other sites to theirs while making the assumption that google's backlinks indexed to the site are similar.
Google doesn't show any backlinks from other website's to yours. Another factor with google, their results are delayed by a few months usually.
Backlinks, and the quality which isn't measured or discussed here, are important because search engines not only consider the content on your page but also who, how many, how popular links are from other sites to yours.
All of this information can be checked directly yourself, without using the software - it just pulls these searches - as with the alexa and google backlink example provided above.