The purpose of a manometer for a mash tun application is to monitor the pressure differential or suction within and across the grain bed.
The manometer offers a visual representation of how fast you are drawing wort through the grain bed, based on the difference in level between the two tubes. When you get a number of brews under your belt on the 20 gal InfuSsion Mash Tun (2016), you will have a better idea of how to set your pump speed and what your lautering performance should be based on the manometer's reading. They are also convenient because they double as a sight glass.
In real-world applications, they give you insight into adjusting the crush of your grain juxtaposed with your efficiency numbers. Until recently they have really only been included with pro equipment to keep things simple. However, we feel that offering more homebrewers pro tools will contribute to the evolution of our craft!