Quite simply, the time it takes for a sound to occur from beginning to end. 
We can also speak of the duration of particular parts of a sound's envelope such as onset duration or decay duration. Duration is measured in minutes, seconds, or some division thereof. 
Duration is related to the perception of both loudness and pitch. 
With respect to pitch a minimum duration of about 12-15 milliseconds is required for a tone (at 1000 Hz)to be heard as a tone at all. If the duration of the tone is any shorter the resulting sensation will be of a "click" without a recognizable pitch. This minimum duration is inversely proportional to the frequency. The higher the frequency, the more cycles in a given duration, the easier it is to perceive a pitch versus a "click". In the case of loudness, beginning at about half a second (500 ms) the perceived loudness of a tone will decrease as the duration of the tone decreases.