Whereas an analog recording is stored on a medium that allows a continuous curve of changing sound pressure values a digital recording does not. Digital recordings are a series of snap shots of the sound pressure at a precise instant stored as a number, as digits in a computer. In a digital recording you can find two points right next to each other for which there is no value between them. A digital recording would be best graphed as a series of stair steps since it is not known what the values are between the points where the sound pressure was actually measured. If you add to that the fact that the equipment that plays back digital recordings does some guess work to recreate the missing points in between each actually measured point you can get a pretty detailed picture of the sound with digital recording even though you didn't actually constantly measure the changes in sound pressure the way you would in analog recording.
Digital recording has several major advantages over analog recording.
Digital recordings are numbers which means they can be manipulated by computers. They can be stored as a list of numbers which will stay the same quality from copy to copy so long as nobody changes the numbers. Analog recordings lose some detail and gain some inaccuracies with each subsequent copy. With our present technology we are able to make and play back more accurate recordings using digital technology than analog. In digital recording there are some decisions to be made that don't apply to analog.