When people sleep invariably they do not “hear” nearly as much as when they are awake. Loud noises generally can wake people up but folks have been known to even sleep through their smoke alarms. When we are asleep are we still hearing everything but our brain simply doesn’t process it, or do we actually shut down our hearing to some degree. Or am I make a distinction without a difference here?
I believe that you still hear the sounds–that is, the sound waves still impact on your eardrums in the same way–but that your brain decides which sounds to ignore and which sounds mean “wake up NOW!”
I know that as a new mother, it took me about a week for me to learn to wake up when the baby cried in the middle of the night, but after that, I was sensitized, and had no trouble coming fully awake and out of bed at the first wail from the other room.
I do not have any factual (schooling or book learning) about this but do have some personal experience which has caused me to think about this subject. I snore and at times it can be quite loud. There have been a number of occasions where I have been in the midst of falling asleep and my wife nudges me to get me to turn onto my side to stop the snoring. The thing is that I don’t hear it at all. I am semi-conscious, and know that I’m breathing heavily, but can’t hear it at all. From my experience it appears that the ears disconnect (or the brain ignores expected noises), at least for a while, so that I can’t hear my own heavy breathing or snoring while asleep or in the process of falling asleep.
As Duck Duck Goose indicates, you get used to sounds and the brain does not react to them while you are asleep. My parents used to live near some railroad tracks. When I would go home during university the night train whistle would always wake me up the first time but not on subsequent nights. I’ve seen this with my cats. Regular noises don’t disturb them when they’re sleeping, but a new (unexpected) noise will startle them awake.
I am curious about the actual physiological explanations for my observations.
I don’t have any particular expert knowledge in the field but have read about it. All of the physical pathways for sensory perception are intact during sleep but there some part of the brain (no idea how this actually works) acts as a sentry, deciding whether to escalate the sensations to some higher cognitive function. Since experts do not even all agree on what “higher cognitive functions” are or how they work (i.e., “consciousness”), this may be difficult to get thorough answers for.
But that’s what explains Mycroft H.'s experiences, and why a city boy can sleep through car horns but wakes up to birds chirping. The OP asks about hearing but the same is true of all the other senses. Bright lights, the smell of smoke, or something crawling on you can all wake you up, or you can get used to them if they are routine and benign.
I’ve also noticed, other than being only sensitive to specific noises, that I can wake up a few seconds before my hearing “wakes up.” In other words, I’ll be awake and conscious, but my hearing will sort-of fade-in. For example, I like to fall asleep with the radio on. I’ll wake up in the middle of the night, open my eyes, see the time on the clock, and the sound will fade-in about a second or two later. I can literally feel my hearing come to its senses.
A strange experience for me is when I hear something in real-life and that noise gets incorporated into my dream, like a phone in my bedroom being translated into a phone ringing in my dream.
I sleep through thunderstorms, but woke up during the 1987 English hurricane because in addition tiles were being stripped off my roof. :eek:
Well, if you arflying a small plane and you want someone in the back to wake up, you can try to yell over the engine noise or just pull the engine to idle. They wake up every time then without having to yell at all. :evil:
I know what happens to mine… earplugs. 
Which is exactly why I cannot use my radio for an alarm clock. It took me way too long to figure this out.
Here’s a question for you: Have you ever been talking with somebody at a party when two people who are having a separate conversation mention your name? It kind of grabs your attention even though you weren’t listening. So it seems that all kinds of sounds are picked up by your ears and processed by your brain without much awareness on your part. I would guess it’s a similar process when you are asleep.
When I was about 11, my parents had a local radio station playing, which at the time included a chorus of adults singing a verse of “America, the Beautiful.” This got incorporated into my dream, so that at the start I dreamed I was lying on my back on the grand piano on the stage in our school auditorium, and by the time they sang “From sea to shining sea” I was standing on the ground looking at a large nbumber of airplanes flyng overhead in military formation.
My husband and I use separate alarm clocks to wake up in the morning, because he wakes up about an hour before I do.
I always am amazed by the fact that I can sleep right through his alarm clock, but am awoken an hour later by the EXACT same beeping from my alarm clock.
That has happened to me before as well. I’ve woken up with the the TV on before and even had enough time to look at and register that it’s on before hearing it.
I can related to what I guess we can only refer to as selective filtering of sounds.
When I moved out to a house I bought in central Iowa, it was located fairly close to railroad tracks. There is definitely something psychological about living in a new place or environment, because at first I was super-sensitive to all the sounds around me:
Every time a train would roll by I would jolt awake, ready. Eventually I got used to it I could sleep right through them even with the windows open. Only when they make that earthh shattering rumble while applying brakes will I still be disturbed
All the other sounds around the house: the fridge coming on, squirrels running around on the roof the sump pump coming on in the basement. All these sounds were new and unfamiliar and every time I heard them they would wake me up, no matter now slight. Eventually my mind learned to recognize them all, i.e. “oh that’s just the sump pump” and I slept like a baby. Only during something unusual (violent storm, something going pop, clunk, or crash) will I wake up.
on the subject of hearing fading in: I can relate but it happens with my vision. I have an alarm clock by my bed with a digital display. I can remember time and time again waking up and looking at the display, and at first it looks like total incomprehensible garbage. I have to blink a few times to clear the cobwebs and suddenly the display stops looking like hieroglyphics and like recognizeable numbers again 
Randomly related - I’ve noticed that if I watching TV or listening to music at a normal volume and fall asleep to it, when I wake up, the volume seems unbearably loud. Seems as though the sensitivity is reset during sleep. I’ve also noticed that sometimes ambient sounds will work their way into my dreams (as well as other sensations such as that of having to pee).