The primary visual cortex is located at the back of the occipital lobe, in the cerebral cortex. If any part of it is destroyed, this will cause cortical blindness in the cross-lateral visual field. For example, destruction of the visual cortex of the right hemisphere causes blindness in the left visual field.
A person with cortical blindness may have perfectly normal eyes, which can move, have pupils which respond to changing light conditions, and exhibit other normal reflexes. They will, however, be completely unable to see anything in the affected visual field. Furthermore, they will not be able to remember this visual field in their memories, nor experience any other visual imagery in the affected field. For example, a person with damage to the visual cortex in the right hemisphere will not be able to recall the left side of any memories, and will be unable to imagine, or dream, anything in their left visual field.
Contrast this with a person who is blind in one eye following severe damage to the eye itself: They will be able to see in both visual fields (but with only one eye, of course); their memories and visual imagery will be unaffected. A totally blind person with damage to both eyes will still be able to imagine visual scenes and recall memories, providing they had previous visual experiences.
Here comes the best part:
A person with cortical blindness may sometimes be capable of feats such as pointing towards an object that is in their blind spot, and that they cannot consciously see; or identifying a simple shape when asked to guess what shape is in front of them. This can be done with surprising accuracy, but not all patients show this type of behavior. This ability is called blindsight and its causes are discussed in the relevant node.
"Biological Psychology", James W. Kalat (7th Edition), pp. 103