This has appeared in Question 15.3 from the first paper of 2012, and in Question 22.1 from the first paper of 2010. In brief, it is a plastic mask with a bag acting as an oxygen reservoir, which is held affixed to the patient's face with elastic. The defining feature of this device is the presence of unidirectional valves. When the patient inhales, the valves prevent the inspiration of room air - the patient will only breathe from the oxygen reservoir. When the patient exhales these valves prevent the movement of expired gas back into the reservoir, so as to prevent the re-breathing of expired gas (hence "non-rebreather").
The actual college description is as follows:
Garcia, Juan A., et al. "The oxygen concentrations delivered by different oxygen therapy systems." CHEST Journal 128.4_MeetingAbstracts (2005): 389S-b.
Abe, Yukiko, et al. "The efficacy of an oxygen mask with reservoir bag in patients with respiratory failure." The Tokai journal of experimental and clinical medicine 35.4 (2010): 144-147.