Fundamental law of Electromagnetics: A current induces a voltage (an electric field, really), and a voltage induces a current. All electronic devices are powered or "driven" by both voltage (a potential difference) and a current (electrons moving in response to that potential difference).
The difference between high impedance and low impedance loudspeakers is that the former requires a high(er) voltage in order to move the electrons while the latter requires a high(er) current demanded by the low resistance to the flow of electrons.