Analogue carries a signal that's a direct version of the sound waveform - in simple terms, for example, a louder sound means a stronger signal.
Digital samples the signal to create a representation in the forms of thousands of on/off pulses, which are converted back into analogue before being sent to the speakers.
Analogue requires one cable per channel, or at least one pair of conductors in a multiconductor cable, such a a headphone cable. Digital, however, can carry two, six, eight or in fact however many channels you want down a single pair of conductors, or over a fibre optic connection. The channels are combined into a single digital datastream, then decoded out again at the other end of the cable.