We did this in the army only once, during bootcamp. The rifle, an M16 was placed on the ground in some kind of frame that kept it in place. We were then instructed to go prone and look through the sights. The rifle was pointed to a piece of paper. There, another soldier with a spoon like thing with a hole in the middle would move the spoon according to our instructions until the hole was lined up with the gun sights. Then he would mark the spot on the paper.
We repeated that process two more times. Apparently the three marks on the paper shouldn’t be too far apart else it indicated some problem with our stance or something.
The purpose is to train the shooter in proper sight alignment and sight picture. If the shooter is placing his cheek in the same location on the stock every time, aligning the sights consistently, and aiming at the same location each time, then the marks on the paper should be right on top of each other. If they are too far apart, then the shooter is not aiming consistently and will never successfully zero.
Possibly just a fundamentals exercise, or possibly they are training to transition from one target to the next. There might be multiple targets which are not in view. If they are preparing for a particular pop-up range, the man holding the targets can make them go up and down, allowing the ‘shooter’ to practice his body position and efficient target transitions.
