I'm just curious, what the business model is for providing these data mining services for free to everyone?
Google made over $28B last year in advertising revenue. Anything they can to make it easier and more effective for people to buy AdWords improves their bottom line. The better the results people see from buying their advertising, the more of it they will buy and the more money Google will make.
This is the same business model many companies use when they conduct free training or give away "how to" guides. For example, Home Depot offers free classes on how to tile a bathroom or lay carpet. The idea is that 1) you're more likely to tackle your first project armed with this training, 2) you're more likely to buy from Home Depot if they've given you this free training, and 3) if the project goes well because of the instruction you've received, you're more likely to try another project in the future.
Projects like those usually come from Google Labs and employee 20% time. Something an employee made to satisfy an internal need, or just to build something fun. If it works and is cool they often release it. Some initiatives flop (Wave) some are huge (Gmail)
Monetization usually isn't considered early on for them, and now it's just if they can Adwords it or charge a fee like Google Apps for business.
I suspect that calculating correlations of all sort is what they do internally to rank pages. This is just a fun way to show some of the correlations in "anonymous" way. By anonymous I mean they usually show no meaningful information on Y axes or it is rescaled.