Theseus
Philostrate
A eunuch is a man, generally a slave or servant, whose testicles have been intentionally removed in order for him to serve some specified role. The word "eunuch" comes from the ancient Greek phrase for "bedroom guard" because in those ancient kingdoms where the ruler maintained a harem of women for his personal sexual pleasure, eunuchs often served as the guards — the thinking being that they would not be tempted to molest those whom they were guarding.
Another group of eunuchs were young boys who had been castrated before their voices had changed, allowing them to sing in a beautiful high voice even as adults. This is the kind of eunuch to whom Lysander is referring.
It wasn’t just ancient despots who had young boys castrated to preserve their high voices. In modern opera-crazed Italy, some overly ambitious parents had their sons castrated, hoping that it would lead to a successful singing career. (If your parents force you to take piano lessons, just think — it could be worse.) This practice was only outlawed in 1861, and the last of these castrati as they were called was still recording into the 20th century.