The Analog Visibilty Controller is intended to give control similar to the AnalogValueDisplay. Most controls you can change the visibility using a Boolean/bit in the PLC, but the AnalogValueDisplay will let you use a number and set the limits of when to display. This can be useful for things such as showing an alarm message when a value exceeds a certain limit.
The AnalogVisibilityController does the same thing but let you indicate which object to change its visibility. If you have a group of objects, they can be placed on a Panel or GroupBox, then the AnalogVisibilityController can control the visibility of the group.