。
Be quiet.
Literal
Be-silent-stay-[command-なさい].
Bare ~ていなさい command — a minimal example of how Japanese softens an order: the ~なさい form is firmer than ~てください but warmer than the bare imperative. Combined with 黙る's ~ている form, it asks the listener to remain silent over a stretch of time, not just to fall silent at one moment.