What does “you’ve been keeping him quiet” mean?

Hearing about her friend’s new boyfriend, one woman says, “You’ve been keeping him very quiet.” She isn’t talking about noise. To keep someone quiet here means: you didn’t tell anyone about this person, you kept it a secret. It’s a gentle, friendly accusation: “why didn’t you mention him sooner?”

“Quiet” usually describes sound, but English also uses it for information you hold back: “keep something quiet” means not telling people about it, whether it’s news, a plan, or, as here, a new relationship. You’ll also hear “keep it quiet” for a secret in general: “Keep it quiet, but we’re moving next month.”