In all hearing aids sound enters through a microphone. It is then processed and amplified and delivered to a receiver (loudspeaker). This sends the output either directly to the user's ear canal, or via tubing to an earmold and into the ear canal. 

In an analog hearing aid the original acoustic signal is processed as an electrical signal. In a digital hearing aid, however, the acoustic signal is converted into digits (0, 1), processed within the hearing aid, and then reconverted to an analog acoustic signal for the listener.

Analog sound processing
Analog sound processing basically means that the movements in the air that make up sound are translated into one unified, but complex, electrical current by a microphone. 

Analog sound is like making a photocopy - the sound is registered and you get an overall picture. But the actual processing is like recopying a photocopy - it can only be done to a certain extent because it causes a deterioration of the original imprint.

Digital sound processing
With digital sound processing, the sound is registered mathematically. It is encoded as a series of numbers that measure its pitch and volume at a given instant in time. Processing the sound bit by bit is much more precise, and certain details can be changed without affecting the overall picture. 

Being more robust than an analog signal, a digital signal can be repeated accurately and endlessly without affecting the overall quality. It's like making copies of a scanned image on a software diskette: each copy is a perfect duplicate of the original.