Six universities were funded as super computing sites. We're talking about the kind of giant computers that you could use to simulate Hurricane Andrew or something else really complex. Money was provided to allow other universities to link up to these sites. Keep in mind that no one agency is in charge of the Internet. It's more like a federation.
Institutions pay a fee to their respective network center and agree to agree.
As a student, you don't receive a bill for your Internet usage at the University. Therefore there's a sensation to you as a user that it's free. However, that's not strictly true. The institution is paying the fee. In this case you may have to pay the connection fees charged by a commercial internet service provider.