The book is imprecise because there are other types of polarized light. Now, consider a point in the path of the wave, like the green point in animation you mentioned. In that image, the light is linearly polarized so the electric field draws a line at the location of the point. However, there is also circularly polarized light where the electric field draws a circle as in this picture

Then, light is said to be polarized if the electric field at a given point draws a line, a circle, or in general, an ellipse. Unpolarized light occurs when you have many of these waves superimposed which results in an electric field that oscillates randomly in all directions.

The book is imprecise because there are other types of polarized light. Now, consider a point in the path of the wave, like the green point in animation you mentioned. In that image, the light is linearly polarized so the electric field draws a line at the location of the point. However, there is also circularly polarized light where the electric field draws a circle as in this picture

Then, light is said to be polarized if the electric field at a given point draws a line, a circle, or in general, an ellipse. Unpolarized light occurs when you have many of these waves superimposed, which, results in an electric field that oscillates randomly in all directions.

This occurs whenever the source is a set of electrons which themselves oscillate in random directions such as in a hot wire.