What were the Eunuchs exactly!?

[Epictetus]

There seems to have been an idea that eunuchs were prevalent in the Byzantine Empire and not in during the height of the Empire. Some Victorian writers (and others) have implied this was a sign of their moral and social degradation. But I wonder about this. Lucian says that the emperor Lucius Verus' mistress Panthea had them in the middle of the 2nd century:

...She received much attention, kept splendid state in every way, had a number of eunuchs and a great many maids, and, in general, the thing seemed to be on a greater scale than accords with private station.

Lucian, Essays in Portraiture