To ensure adequate blood oxygenation, the masks & regulators have a feature called “positive pressure breathing.”
At high altitude, simply inhaling even pure oxygen won’t get enough into the bloodstream to keep the brain & body working well enough. So the regulator has a device to detect ambient altitude (cabin air pressure really) and force oxygen at fairly high pressure into the mask.
That will only be effective at ramming oxygen into the lungs if none of it leaks around where the mask fits the face. So the head harness is a pretty stout thing which is adjusted to fit uncomfortably tightly. The face-sucker is clamped tightly over your nose/mouth & when it’s in positive pressure mode it’s a real PITA to breath. Unlike normal everyday life it takes positive effort to exhale & with just a slight relaxation of that effort the mask will inflate your chest like a balloon. Normal breathing is pull gently, relax, pull gently, relax, … . Pressure breathing is relax, push HARD, relax, push HARD, … It’s difficult to talk intelligibly while pressure breathing.
The mask is designed to be able to be put on using one hand in just a couple seconds. At very high altitude and with a very rapid loss of pressure (= big hole in the airplane), you may only be conscious for 5-10 seconds total. Gotta be quick. Or be dead. And it has to fit over headsets and / or eyeglasses.
Older designs were a rigid plastic frame with some hinges & springs; you’d hook the frame benind your head & then pull the facemask forward against spring pressure & down over your forehead to place it over your nose / mouth. Then release it back to let the springs relax a bit but still smash it into your face. Ideally you didn’t sweep your glasses off onto the floor with the same motion.
More modern designs dispense with the plastic frame and instead have a harness of flexible rubber (surgical) tubing. When you grab it to put it on, you squeeze a lever which inflates the tubing making the harness rigid & much bigger than your head. It’s easy to push the mask directly onto your face & the harness ends up around & behind your head. When you let go, the tubing deflates & shrinks down to tightly conform to your head, securing the mask in place for for pressure breathing.
As **Richard Pearse **explained, older set ups include separate smoke goggles which are sorta like snorkelling masks. Deep enough to have room for eyegalsses & with a fairly large opening to provide some semblance of peripheral vision. They too are held onto the head by heavy elastic straps to ensure a smoke-proof fit against a face. Those go over the oxygen mask harness & are uncomfortable & unwieldy as hell.
Some of the lastest designs incorporate the smoke mask & oxygen feed in one unit; these look a lot like the gear you see modern firefighters wear.
Here are some thumbnail pix of various models. http://www.aviationoxygen.com/delivery_above_25000.html
The one at upper right demonstrates a mask plus separate smoke goggles. The rightmost 3 in the bottom row are typical latest-and-greatest airline units both with & without smoke masks and using the inflating tube harness. The one at bottom left is standard military gear; not relevant for airline use.