Having seen these little keyword-entry boxes on almost every site where you sign up for anything for quite a while, this isn't exactly NEW to me, but I never quite realized how Recaptcha works.
Here's the low-tech background: When you scan a book or other literature with a scanner, the computer can't read the text - the scanner basically takes a "picture" of the book page.
There are programs that usually come free with your scanner, or you can buy more fully-featured versions, that attempt to "read" the "picture" of the book page. These are called OCR (Optical Character Recognition) programs. They are improving, slowly, incrementally, but most are in generally really, REALLY bad and make a ton of mistakes.
It turns out that the best reading "technology" is right up here in our heads.
So the folks at ReCaptcha are using our heads, for free, while providing two valuable services for free: stopping spam sign-ups for various sites, and digitizing a wealth of offline literature. They do this by making 2-word portions of scanned documents into "passwords" that you must type correctly to be allowed access to whatever it is that you're trying to access.
This works much the same way as Google's image labeler game, getting people to sometimes unknowingly "donate" tiny wasted-anyway fragments of their time for free in return for something they desire (in Google's case, playing a game, for ReCaptcha, access to websites and accounts).
How much better does the human brain work than current OCR software technology? See this page for sample scanned texts.
And here was my big question... if they are using your mind to find out what the scanned text/image says, how do they know you are typing it right? Here's a whole page that will explain better than I ever could!
Take a minute to play with a few ReCaptchas just for fun while you're there... you'll be helping digitize the wealth of human knowledge!