Active noise cancelling headphones differ from pair to pair. They have microphones on the outside of the headphone, and the circuitry in the headphone creates a sound whose signature (as in it's sound wave) is the polar opposite of the noise it receives. This sound, when combined with the incoming sound and passed into your ear has the effect of making things sound quieter. They're all pretty good with low frequency noises, because the generated sound wave doesn't have to be quite as precise in order to cancel the incoming sound, mainly because the sound waves are longer (hence lower frequency). High frequency noises can sometimes have some issues. For example, the Bose QC15 can pretty much eliminate the sound of an airplane engine, but you'll still hear the hiss of the air valve over your head, and you'd better hope you don't have an infant sitting behind you.
So, because the circuitry can be somewhat "selective" about what it wants to block and what it won't block, many of them are made to block ambient noises but not to block sounds coming in at the same general wavelength as a human's voice.
It can help to protect hearing, in that you'll probably keep your music down, but more than that, exposure to sudden volumes over 70 dB or constant volumes over 110 dB is thought to affect the autonomic nervous system (fight or flight). Airplane cabins seem to run around 95-105 dB, which, in my mind, is loud enough. Some of this is speculative, however. I did spend some time trying to find a good journal article or something that would prove the point, but I had a very hard time finding good hard evidence that volumes over a specific dB level actually have these supposed effects.
What I can say, however, is that I feel far more fatigued if I've been on a plane for a few hours without some kind of noise attenuation. I think most people experience this. I have a pair of Bose QC3s. The sound is... well... acceptable, but the noise cancelling is excellent. I've seen the QC15's, and those are supposedly even better. I feel far less fatigued after a flight if I've worn these headphones for the duration of the flight than if I don't wear them.
In a couple of weeks, I'll be headed to Seattle, and I'm planning on wearing my IEMs for the duration of the flights. We'll see if simple noise isolating IEMs has the same effect as the noise-cancelling headphones.