Conventional communications systems use forms of modulation of the carrier that are considered 'analog' in nature. The amplitude of the carrier is modulated in a continuous fashion in AM communications systems. The frequency of the carrier is modulated in a continuous fashion in FM communications systems.
Digital modulation involves modulating the carrier in discrete steps -- either in amplitude, frequency, phase, or all three depending on the type of system. Most of the time the analog signal is coded into numbers and the numbers are transmitted as the discrete steps on the carrier.
Listening to a digital transmission on an AM or FM receiver may sound like anything from whistling to pure hissing noise.