Inner silence occurs when the verbal chatter of the mind, the self-talk, stops. This can be brought about by meditational practices. Though I must admit to only having experienced it for fairly long periods of time, whilst undertaking long, e.g. nine and ten day meditational retreats where one meditates for maybe ten and eleven hours a day.
For shorter periods, however, it is possible for these to occur spontaneously. This is one reason why people like to travel and experience new things. In that moment of discovery, when one is looking, the mind-chatter often stops. But it generally doesn't last, as the ego-mind (the conditioned evaluating part of ourselves) goes into its diatribe of like:dislike, good:bad, etc..