Can someone please explain this type of vector to me, I can not understand it.
Axial vectors have an inner orientation, i.e. the direction of the vector indicates the positive orientation. For example, a unit linear force vector: the positive direction of the force does not depend on the orientation (right-handed vs. left-handed) of the world reference frame. As many (but not all) other textbooks, this book implicitly uses right-handed reference frames only, but no physical arguments prevent the use of left-handed frames.
Polar vectors have an outer orientation, i.e. the positive orientation cannot be derived from the direction vector itself, but is imposed on it by the environment." For example, a unit moment of force vector: if the handedness of the world frame changes, the orientation associated with the moment vector changes too. Note that this is a feature of the coordinate representation, not of the physical property that the vector stands for.