When you emasculate something, you take away its strength. The elimination of foreign language classes at your local high school could emasculate, or terribly weaken, the school's academic reputation.
The Latin emasculatus literally means "to castrate," though it is usually used figuratively, the same way emasculate is sometimes used to suggest a man isn't very manly. You may have seen bullies hassle a guy, saying he can't beat up anyone, or hit a curveball, or. . .you get the idea. Such emasculating is also insulting to women because it suggests strength and female are opposites.