They are the system for the flight data. The airlines submit their routing information to ITA and ITA provides the search functionality for most of the travel websites and agencies you use.
As others have said, they don't have every airline, and there are other route search companies, but they are one of the biggest.
As for the queries, airline routes and their pricing is extremely complicated. Their matrix software has been getting better over the years, and it does add new features every once in a while. But as for it being "a great tool... with a [potential] business model", that's what they're doing at ITA. If you've got some great query ideas, go see them. They're always hiring, their recruitment ads are all over boston.