The decay time is the time it takes for a voltage or current pulse to decay to one tenth of its maximum value. The decay time is proportional to the time constant of the circuit.
In audio, decay time is an important parameter of reverberators. It is also called Reverberation Time( RT) and determines the duration of the reverberation. Since the reverberation is frequency-dependent, it can be set separately for the duration of the reverb and for the treble and bass.