。
She signaled me to keep quiet.
Literal
She [topic-は] me [to-に] keeping-silent [in-order-to-ように] signaled.
黙っている is the ~ている form of 黙る ('be silent, hush'), marking the sustained state of silence. ~ように合図する ('signal (someone) to do X') uses ~ように as 'so that, in such a way as to' attached to the desired outcome — here, the sustained silence. に on 私 marks the recipient of the signal. 合図 ('signal') is a Sino-Japanese noun used both alone and with する.