According to Wikipedia "Earcup headphones
Earcup or on-ear headphones rest on the exterior of the ear and were the earliest headphone form designed.
The housing, or earcup, of an earcup headphone will be either open or closed. Open headphones, sometimes marketed as “open air” headphones, have an open grille on the back of the earcup, exposing the driver to the outside and allowing sound waves to propagate away from the ear freely. This backing type does not isolate the listener from outside sounds; in addition, sound through open headphones can be heard by others in the vicinity of the user. They usually have less distortion due to the lack of earcup resonance. Closed headphones have a sealed backing, which attenuates sound waves propagating away from the ear. As a result, listeners away from the headphones cannot hear the produced sound easily. In addition, sound from outside is attenuated by the sealed backing, providing a level of isolation to the listener. A sealed chamber is often claimed to have the negative effect of distorting sound in certain frequencies due to resonances within the earcup housing, however, bass frequencies are stronger in a sealed chamber headphone design."
You want closed headphones because you don't want sound leaking out and being recorded by the machines. That is what I am assuming.