Hello
An ADC in the ordinary sense is usually a Captain (in the army), and is attached to a specific senior officer. He accompanies him on his official visits and generally 'smoothes his path'. In the British Army, he comes from the same regiment as the General concerned, and is either hand-picked by him or is recommended to him by someone who knows them both.
A friend of mine, then in the TA, found himself spending an afternoon acting as ADC to the Colonel of his regiment, the by then very aged Field Marshal Sir John Harding, at a presentation of new colours. The highlight of all this was being told, 'Here, hang on to this bloody thing!' The bloody thing was the Field Marshal's baton!
Being an ADC to a monarch is rather more complicated, as monarchs usually have both 'ordinary' ADCs (termed equerries in Britain), and senior officers appointed as more honorary ADCs (usually termed General ADCs). The General ADCs will not be running around making sure that the Great Man's staff car will be ready to pick him up, but will greet the monarch when he arrives for a visit, accompany him round, etc.
Hope that helps
Ann