I can give it a shot.
Here is an image which clearly illustrates what your book is telling you.
First lets define some words. Medial or nasal means towards the middle, or closer to your nose. Lateral or temporal means towards the sides or closer to your temporal bone.
Lets consider this situations. A doctor shines a light in your eyes on your left side. Light from the light bulb travels to your eyes and hits both of your retinas. Because its coming from the left, it doesnt hit the entire retina on either side. In your left eye, the light hits your medial, or nasal, retina. In your right eye, the light hits your lateral, or temporal retina.
If you look on that diagram, you see that the nerve fibers from both medial retinas cross at the optic chiasm, and continue in the opposite side of the brain. Because of this, information from the left side of both eyes travels to the right brain. Similarly, information from the right side of both eyes travels to the left brain.
So while yes, both eyes are connected to both hemispheres, information from the left and right sides of your visual field go to the right and left hemispheres, respectively.
At the occipital lobe, the rearmost part of the brain, the information received from the retinas is processed, and your brain attributes “what”, “where”, and “how do I feel about this” to the things that you see. Without the occipital lobe, your brain can’t understand the information it receives. Losing the occipital lobe is sort of like trying to stream a video with the wrong codec. You get all the raw information, but you have no way to interpret it.
Interestingly, lesions of the occipital lobe can cause a phenomena known as cortical blindness. Patients will swear up and down that they can see just fine, but will be unable to tell you what they are seeing. You can predict what areas of their visual field will be affected by the extent of the lesion.
So yeah, that diagram explains it all pretty well. The corpus callosum is not involved with vision until after it has been processed by the occipital love.