Digital audio uses digital signals for sound reproduction. This includes analog-to-digital conversion, digital-to-analog conversion, storage, and transmission. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. While modern systems can be quite subtle in their methods, the primary usefulness of a digital system is that, due to its discrete (in both time and amplitude) nature, signals can be corrected, once they are digital, without loss, and the digital signal can be reconstituted. The discreteness in both time and amplitude is key to this reconstitution, which is unavailable for a signal in which at least one of time or amplitude is continuous. While the hybrid systems (part discrete, part continuous) exist, they are no longer used for new modern systems. 
(Reference: http://en.wikipedia.org/wiki/Digital_sound)