an analogue datastream will have the data carried in a form where it can have a variable value and be represented by a variable point on the y axis of a graph (the x axis usually being time). So for music, the waveform of the music is represented more or less exactly by the waveform of the transmitted data.
a digital datastream will simply contain a stream of data in the form of points which are either 0 or 1, yes or no, black or white. At some point that stream of ones and zeros will need converting into an analogue form by some flavour of ADC before we can relate it to music or picture or whatever.
Simple so far, however if we get into the realms of quantum physics, the boundaries are much less clear.
Film can be viewed as both analogue and digital. Digital because the picture is captured as a series of dots or grains, which we then see as an integrated smooth whole, analogue because each dot can receive a signal of different intensity and give a directly proportional chemical reaction.
See, simple!