This is a communicaitons system eartube, universally shaped for use by astronaut but assigned for Apollo 11 to astronaut Buzz Aldrin. It allowed him to easily and comfortably hear transmissions from Mission Control during the mission while he was in the command module. When in use, they connected to the earphone of the lightweight headset. When not in use, they could be stored in the pocket of Aldrin's inflight coverall garment.
NASA transferred these eartubes to the Museum in 1970 with other Apollo 11 equipment.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.