I love the Straight Dope:
Q: I have asked flight attendants on airplanes all over the world. No one knows. No one even hazards a wild guess. ... Why doesn't the plastic bag inflate? Since it doesn't, what is it for?
First an inside secret: the bag does inflate, but only when you exhale.
Here's the deal. Passenger oxygen masks give you a continuous flow of oxygen (as opposed to oxygen on demand, which only flows when you inhale). The oxygen obviously can't flow into your lungs while you're exhaling, so if there weren't some way to store it temporarily it would have to be vented wastefully. The bag makes this unnecessary. When you start exhaling, your breath plus the incoming O2 flow into the bag.
Cecil Adams rocks.