PWM signaling with Arduinos: What is the reason for the ground connection?
Is PWM really a signal? To me, it looks like an electric current turned on and kept on for a certain time, then off for a while repeatedly. What makes this a "signal"?


At the most basic, it is a signal because we call it such. Even a constant voltage can be a signal, signalling that e.g. a window has not been broken. A PWM signal indicates that we want to apply a certain fraction of full power to a load.


  If PWM is a signal, why do we need to connect the Ground from Arduino to the ground of the device to which "PWM signal" is being sent to?


Because it is a voltage-based signal, and ground serves as the reference for this voltage. Voltage only exists between two points.


  This is confusing me because in my mind, for example, radio signals do not need a ground connection. The signal comes and gets read.


Radio signals are photon-based; the oscillation of photons at a given frequency being broadcast from a location are what define the signal. Since frequencies are absolute, they can be discriminated without a (relative) reference.