So what is YQL? YQL looks like SQL but enables you to access live data from the Internet. That definition doesn't really do it justice, however. The bigger point about YQL is that it includes many built-in bindings to various web APIs so that you can use almost every major web API in a consistent manner, with similar calls across the many possible APIs available to you.
Yahoo uses APIs for nearly all of its products. Instead of accessing a database and displaying the information live on the screen, the front end calls an API, which in turn gets the information from the back end, which talks to databases. This gives Yahoo the benefit of being able to scale to millions of users and being able to change either the front or back end without disrupting the other.
Offering your content or logic as a service on the web is a great idea. For starters it allows you to build numerous front-ends for your own information without having to access the databases all the time (and thus making scaling your system much easier).