Technorati's "Authority" number is similar in concept to Alexa's ranking and Google's Page Rank (Google PR). Alexa's is the easiest to manipulate, PR is the hardest to manipulate. Alexa's ranking is semi-worthless as a true ranking tool, though it is the standard many companies use to rate blogs. Google PR is the gold standard, but it has it's faults.
On the other hand, while not used by many for rating blogs, Technorati Authority is a potentially better way to rank blogs and is not as easy to manipulate as Alexa.
Page rank is a log scale number from 0 to 10 that tells how popular an individual web page is based on how many web pages link to it. Authority is a similar popularity contest but is a gauge for the entire blog site, not just a single web page. If nothing changes, PageRank lasts forever while Authority is only good for links made within the last 180 days. Also with Authority, only one link (vote) from each blog counts towards the receiving blog. This is unlike Page Rank, which allows many or even every page link to "vote" for a web page.
So a blog with an authority of "2" would have two blogs that link to it. A blog with an Authority of "500" would have 500 blogs linking to it.
Technorati uses Authority to determine search results. So even if it is not a gauge normally used to rate your blog by services such as PayPerPost, with a higher Authority you will get more traffic to your blog. Oh, and the links help increase your Page Rank as well.
Technorati's Authority Checker widget (near the bottom of the page)
Technorati Manual Pinger