Auditory feedback, AKA speech feedback, refers to the processing of speech sounds as they are produced. As you are talking you are also hearing the sounds that you produce, and your brain subconsciously processes them. This gives you real-time feedback of your speech, and you automatically and unwittingly use this feedback to adjust the way you speak, changing your loudness, pitch, and quality of voice to match your learned expectations. We learn these expectations when we are children, and we tend to keep these expectations throughout our lives. (Children from loud families grow up to be loud adults). This can be a problem if our hearing becomes poorer as we age, because we will speak louder and louder until our voice sounds as loud as it should to us. (Of course, you might also lose hearing in the higher frequencies, so that you can still hear speech, but can't understand it; in this case you will not raise your voice, but your speech will become poorer ('cus you can't understand yourself), causing people to complain that you are mumbling.)
An everyday effect of this phenomenon is when you find yourself talking more loudly than you intended when you are talking while listening to music through headphones. Because the loud music makes it more difficult to hear your own speech, you unconsciously increase the volume of your voice until you can hear it clearly above the music.
Delayed auditory feedback (DAF) is a related phenomenon; when the speech coming into your ears is delayed, even by a small amount, it drastically affects your ability to speak fluently. A common cause of this is when you call into a radio show. There is a pause of a couple seconds before your voice makes it through the phone line and back through the radio waves. Many first time callers find themselves unable to speak when they hear their delayed voice coming back at them over the radio -- not because of stage fright, but because their brain is flummoxed by the delayed feedback. For some reason, this effect is more pronounced in males than in females.
DAF is also used in various kinds of research, particularly in research on stuttering. It appears that a delay of even 175ms can cause fluent speakers to become tongue-tied and stutter. This leads to the possibility that stuttering may sometimes be the result of an auditory processing disorder. Oddly enough, a stutterer may become fluent when listening to DAF. (Real time auditory feedback with altered pitch or another voice superimposed over the speaker's may also temporarily 'cure' stuttering). We currently don't know why this might be, but it certainly suggests that there is some auditory processing aspect to fluency disorders.
It is important to note, however, that the types of dysfluencies that are caused by DAF are different than those found in developmental stuttering. DAF disrupted speech causes dysfluencies scattered throughout a person's speech, where stuttering causes dysfluencies occurring at the beginnings of words and phrases. While it is very likely that there is a connection, what exactly this connection may be is still unclear.
Research has shown that effects on fluency can also result from proprioceptive cues, so in some cases stuttering might result from a sensory integration problem. While the study of auditory feedback has been ongoing since the 1950s, the study of proprioceptive and other types of sensory feedback is still in its infancy.
DTal reports that interrogators (and doctors who suspect fakery) use the technique of feeding the subject's speech into their own headphones as a way of telling if someone claiming to be deaf is truly deaf. If you can hear yourself a second delayed, you are completely unable to talk normally.