As I understand it, there's a small chance that certain electronic devices could interfere with the plane's instruments. Realistically, this is extremely unlikely. In practical application, though, the FAA isn't completely sure that a device is safe until it's actually been tested.
And because that would mean testing hundreds of different items, and then restesting each time a new model comes out, it's easier to just do a blanket ban on an entire classification of electronics like "no cell phones".
It's dumb, but it keeps the liability lawyers happy.