Analog uses a direct signal of some sort, eg. mechanical position or voltage in a circuit, to represent the signal being measured or recorded.
Any mechanical or electrical noise existing the equipment adds to the signal and becomes part of it - dust or scratches on a vinyl LP, electrical or tape "hiss" on a recording etc.
In digital equipment, the varying voltage is digitised for storage and processing;
imagine drawing the analog sound voltage waveform on a piece of graph paper, then at regular close intervals noting the exact height of the line above or below zero.
If you re-draw that sequence of points at the same intervals and same heights as you noted down and "join the dots", you re-create the original analog waveform.
That's the essence of digital recording or storage - it's the string of numeric values that is stored & they can be handled just like any other data file - no matter how many times you copy it and whatever the media, as long as the file is not corrupted it will always convert back perfectly to the original analog signal.
You can also do signal processing on it by purely digital (mathematical) means, such as tone filtering or mixing / blending multiple different signals, changing the speed or frequency and many other things, without introducing any noise or distortion that would happen through multiple stages of analog processing.
As long as the sample rate is set high enough (eg. sample points close enough together) and the numeric accuracy of the point "heights" is high enough to get all the waveform without missing any details, the eventual reproduction as analog will be just the same as when it was captured.