The initial idea is to have a Family parameter to switch visibility of elements in a Family depending on the view. So if I have a very detailed Family on the first floor and this Family is visible on the second floor as well, I don't want to see all details of that family on the second floor-view. If I had a view-specific visibility parameter, I could assign this to the Family elements of which I want to control the visibility. On the view first floor, I would switch this parameter on and on the view second floor, I would switch it off. For example, I could create a masking region in the Family to hide stuff I don't want to see in every view and assign it the view-specific visibility parameter.
View-specific parameters can do more than just manage visibility. For example, assign different colors / materials in different views. This would open a whole new level of flexibility.