These special helmets prevent someone's true Psycho-Pass from being visible. They were first invented by Makishima to fool the Sibyl System. It can deceive cymatic scans, allowing criminals to bypass Psycho-Pass scanners and render security bots completely useless. It does this by co-opting the scans of those around them. While fabricating a Psycho-Pass is impossible without massive volumes of computing power, copying them is not. It is not perfect, however, and its range is only 30 meters; so if there is no one around or no one with a clean Psycho-Pass, the helmet makes no difference. Aside from its basic function, it's constructed of solid steel and serves the function of a drill helmet. After the riots, Sibyl modifies the Psycho-Pass scanners to detect a copied reading.
Shinya Kogami is the last one using such a helmet, leveraging it to escape during the time the Psycho-Pass Scanners weren't already updated. The helmet he uses is later found in a waste disposal section in Urayasu and brought back to the MWPSB.