[ijk]

To answer your questions about the context: over-the-air broadcasts generally only include the games for that particular region of the country. (Here's this week's map: http://506sports.com/nfl.php?yr=2013&wk=11 )

Having regional broadcasts allows the sports leagues to essentially sell the games twice: once for the local network and once for the cable network (though I'm sure the actual licencing is more complex than that). Access to all of the games is a selling point for cable, particularly when your favorite team hails from a different region than the one you are currently living in (which is fairly common in the US, particularly since team attachment is often based on where someone grew up or which college they went to).

This setup makes sense for the leagues, since it was based on the limits of the original technology. Aereo removes the technical limits, and is threatening to remove the legal limits.