Acousmatic refers to any sort of sound whose origin is unseen. The sound could be produced by a radio or a telephone or a set of speakers, but the listener would have no visual cue attached. As a result, the listener may try to visualize the source of the sound, with varying degrees of success.
The first recorded use of acousmatic sound was by Pythagoras way back in Ancient Greece. Pythagoras would place a black curtain between him and his audience when giving lectures. He did this so that his students would focus more on his speech than on his person. The word acousmatic comes from the Greek word akousma: what is heard.
The term acousmatic came into usage in the 1950s by Jérôme Peignot in order to describe "a sound that we can hear without knowing its cause" and to designate "the distance that separates a sound from its origins." In 1974, François Bayle described his brand of electronic music as acousmatic music to imply a style that was "shot and developed in the studio, projected in halls, like cinema." The term describes both the medium (which back then was tape) and the esthetic intentions, which are to make the listener think about the sources of the sounds.
Acousmatic sound is used frequently in film for dramatic effect. Any sound that comes from offscreen is acousmatic relative to what is in the shot. One way this is employed is that an image produces a sound onscreen, and then the image is recalled by reproducing the sound later, when the image is offscreen. Another way, which is used in horror films to build suspense, is to produce a sound and keep the source hidden, and then later reveal it dramatically. This is known as de-acousmatization.
The opposite of acousmatic sound is visualized sound: a sound which is accompanied by the sight of its source.
Chion, M. Audio-Vision: Sound on Screen. http://www.filmsound.org/chion/acous.htm
McEvilly, J. 1999. "History of Electro-Acoustic Music." http://acusmatica.7host.com/acousmatique/John.htm