An Eunuch is someone who works in the palace in ancient Korea.
In this case, they are kind of like servants and they usually run the palace's daily affairs.
They can even potentially become political advisers to the emperor.
And yes, one of the requirements to being an eunuch is that you have to be castrated.
There were 2 types of castration in the past. The one where only the balls are cut off and the other (the more common type in ancient East Asia e.g. China, Korea, Japan) was they cut both the balls and the shaft and left only a little portion to let the pee pass. End result was like an engorged female genitalia.
The object was to prevent their ability to impregnate any women in the palace without Emperor's consent as all women including even the maids belong to the Emperor. If they were on the Prince's household they belong to the Prince.
However I nvr heard of Revived Eunuch term as in this comic. Since it's not like what had been cut off could grow back like some octopus' tentacles ( ̄∇ ̄") so
I have read once that sometimes the cut off penis, if done when they were very little, can still grow a bit more but only when it wasnt cut off completely and it wouldn't grow back to normal size.
I'm not sure how in the picture the Eunuch had full normal size dick with balls and no function is lost. My guess is he probably never castrated before?
I still don't get what a Eunuch is :)