All electric motors work by the interaction of two magnetic fields pushing on each other. One field is created by the rotor and one by the stator. The difference between motor types is in how these fields are created and controlled:
EC motors use permanent magnets to create the rotor field, and a series of coils controlled by an electronic controller (or "commutator") to create the stator field.
Brushed DC motors use permanent magnets to create the stator field, and a series of coils powered by the DC input voltage and controlled by mechanical contacts ("brushes") to create the rotor field.
Induction motors use a series of coils powered and controlled by the AC input voltage to create the stator field, and the rotor field is created electromagnetically (or "induced") by the stator field.
EC motors have no brushes, so avoid the sparking and short life of brushed motors. Because they have electronics controlling the stator, and do not need to waste power inducing the rotor field, they give better performance and controllability, and run cooler than induction motors (for small motors, at least: high horsepower 3 phase induction motors can be very efficient). EC motors are used today in many fractional-horsepower applications where high motor efficiency, reliability, and/or controllability is desired.