For example, an entity with a position and a velocity component (position could hold x,y,z values and velocity vx,vy,vz values) could be operated on by a movementSystem (which adds behaviour to any entities that have both a position and velocity component, and updates position values based on velocity values.)
The nice thing about such a system is that the taxonomy as you call it gets defined when you instantiate the systems of your program. If you have entities with position and velocity components but dont want to use a movementsystem to operate on them, you simply dont instantiate the movementsystem. Pretty flexible, but not used excessively outside of video games.