Aide-de-camp is somewhat difficult to describe - (it's like an elephant, you know one when you see him!).
Essentially an ADC is a young officer attached to a senior officer - in the British army an ADC is usully a Captain. He travels about with him, smooths his way and acts as a confidant. He almost always belongs to the great man's own regiment, and being an ADC is a sign that he may well be on the path to greater things.
As far as royalty are concerned, there are two types of ADC. One is the type described above, also known as an equerry (though in Britain an equerry is usually a Major). There will usually be more than one, and they take turns to be 'in attendance' on the monarch. I don't know whether it's still the case, but equerries here used to do two weeks in attendance at a time, as did ladies in waiting. The other is a senior officer who is made a ADC to the monarch as a sort of honorary appointment, though he will attend on the monarch when the monarch visits. A prince, once he reaches a certain age, will usually be made an ADC to the monarch (Prince Charles is an ADC to the Queen, and no doubt Prince William and Prince Harry will become so in due course). One of the arguments put forward by Anna Anderson's supporters was that Grand Duke Andrei Vladimirovich accepted her as Anastasia, and Andrei Vladimirovich was an ADC to Nicholas II, so must have seen her regularly. But Andrei Vladimirovich was an ADC in the honorific sense, not in regular attendance on the Tsar, so that doesn't prove anything. In fact, Andrei Vladimirovich was more-or-less persona non grata at the Alexander Palace, so probably didn't know Anastasia all that well.
An ADC of either kind can be recognised by his aiguillettes - the fancy gold cord things on the right or left shoulder.
Ann