Pure rotational motion means that the body is only rotating. There is no translational motion.
This is an example of a textbook author trying to be very precise. However, without a clear definition of the new terminology, it shouldn't be surprising that a student gets confused.
It appears that some new type of rotational motion is being discussed. It would have been much clearer of the author had said, "a rigid body exhibits only rotational motion," or, "a rigid body is rotating around its center of mass."