If you watch "Medical Dramas" the bags you see there inflate and deflate as the patient breathes.
Different kind of mask...a rebreather mask, vs. the nonrebreather mask in the airplane. Medical administration of oxygen, a drug, is a little difference than emergency supply of oxygen in an airplane.
The bag may or may not inflate. The mask is a simplified non-rebreather mask with a maximum potential delivery rate of about 22 lpm flow. The bag acts as a resorvoir which does two things; it enables a larger volume of oxygen to be drawn with a breath, and it helps prevent flow-through wastage of oxygen between breaths.
How full the bag gets depends on one's rate of breathing. In a time of crisis, one tends to breathe in a panic; it's one of the first controls to go. The crisis claims our breath. That is, our body has been practicing breathing for our entire lifetime, but in a crisis the process of simple respiration is accelerated in a panic. Rather than allowing time for the bag to inflate, we suck the air down as fast as we can...and we see no inflation.
I worked as a firefighter. This involved wearing self contained breathing apparatus...SCBA gear. I've seen firefighters empty a tank in five minutes. It's not hard to do, breathing hard, working hard. It should last about fifteen, and it can, if one breathes carefully and slowly. This takes practice however, and conserving air isn't first and foremost on the average passenger's mind.
Rather than giving a detailed explaination, the briefing is usually "the bag may or may not inflate, but you will be receiving oxygen none the less." As a passenger, you really don't need to know the flow rate or function of the mask. Just that it's delivering oxygen, and that you shouldn't worry if you don't see the bag inflate. You're told that to prepare you...so you don't have to question it later.
The bag does two things, then. Given a little time and a good seal on the mask, it will inflate between breaths. However, if there's no seal on the mask (as often there isn't), then enough oxygen is escaping the the mask that air only flows through the bag, rather than inflating it. Not a big deal. If you do get a good seal, rather than simply letting the pressure build in the mask and then push out and be wasted, the bag acts as a resorvoir. It contains the oxygen between your respirations, allowing it to go unwasted.
It's worth noting that at altitude it's not the amount of oxygen that's important to you; it's the pressure. Vapor at any altitude has a pressure, and for any given altitude, oxygen makes up about 21% of that pressure. At sea level and for most people anything up to 10,000 to 14,000, the partial pressure of the oxygen in the atmosphere is sufficient to pass through the cell walls in your lungs and participate in the respiration process...the exchange of waste materials from your bloodstream for fresh oxygen for your hemoglobin.
At higher altitudes, even though you may be supplied a higher concentration of oxygen, insufficient partial pressure may be available to permit the respiration process. Simply put, the gas (oxygen) is there, but you can't really use it. Never the less, get on it as soon as you can and stay on it. At higher altitudes, the time of useful consciousness is very low, close to 5 to 15 seconds during a rapid decompression. The potential for loss of consciousness is very high, and you'll need that mask on your face as you descend...even if you're not awake for the descent.
You're always told to pull the mask toward you. It took some time to dawn on me that this wasn't just a way of telling me to put the mask on. You must pull the mask because there's a lanyard attached to the mask. This lanyard pulls a pin in the valve assembly above your seat, allowing oxygen to flow to the mask. When the masks deploy, it's done because oxygen pressure has been let into the lines leading to the manifold above your seat, and that oxygen pressure releases the latch. It doesn't provide oxygen to the mask, however, until you pull on it, pulling the pin in the manifold and causing the oxygen to flow. For the masks simply hanging down, there's no oxygen flowing out of them, and you won't see the bags inflate on those either.
Where oxygen is very, very important is smoke in the cabin. You can live without water for days, without food for weeks, and without sex for...unfortunately a very long time. But not oxygen. Just minutes. When synthetics begin to burn they form toxic gasses which range from Phosgene gas to carbon monoxide to hydrochloric acid...which constitutes when the smoke contacts your mucus membranes such as your eyes, nose, mouth, and airway. Smoke can overcome you very quickly, so getting on the oxygen is important. This isn't a time to worry if the oxygen is flowing because the bag looks flat...so you're told in advance that it may or may not inflate.