Spiritually, silence is a ‘space’where there is no need for sound. Many religious orders are silent on the basis that there is then closer communication with God. In dreams it may suggest that contemplation and withdrawal from the everyday world is necessary.
Psychological / Emotional Perspective:
When we are silent in dreams we are unable to voice our feelings or opinions. We are either inhibited by our own selves or by outside influences. Conversely in silence we have no need to express ourselves.
Everyday Material Aspects:
Silence in a dream can suggest uneasiness and expectancy. There is a waiting for something to happen or not. If a dream character is silent when we expect them to speak, we are unsure as to how we ourselves will react in waking life to external circumstances.
You might also like to consult the entries for Hear / Hearing and Sound.