As I have written about previously, I think it is important for Christians to experience intentional periods of silence (http://benedictinelutheran.blogspot.com/2013/06/the-spirituality-of-silence.html). But peace and quiet is only one aspect of silence in the life of a Christian.
Our thoughts can reflect the pace of modern society - our minds jump around from one subject to another, from subjects such as our "to do" list for the day, to mental images from our past, and thinking about news events we have learned about through the media. So, even though we might be in a place where there is silence around us, we are not truly experiencing silence, because we lack interior silence. Our racing minds can sometimes prevent us from being aware of the presence of God in our lives.
A modern day monk who lives at St. Anthony's Monastery, in the deserts of Egypt, spoke about the difference between exterior and interior silence:
"First of all, there are kinds of silence. There is silence and there is silence. Silence can mean not speaking; you are going to stay in a place that is quiet. This is helpful. It's nice to go into a nice forest or a nice garden where you are away from traffic and from talking with people, where you are away from the demands of the modern world. But this is an exterior silence -- which helps you breathe slowly, to enjoy aesthetic pleasure, the beauty of creation -- but it is transient; it will not last.
There is another type of silence, which is interior silence. Now this is much harder to find, but it is long-lasting. For example, memories. Here we are living in the desert; here I am living up there in the mountain. For long periods of time -- two weeks, three weeks, one month -- I don't see any people. I'm not committing sins of action daily. I'm just sitting quietly and working and praying and being alone. What about my mind? My mind can range everywhere. If I don't have interior silence, I can be as busy in mind as if I were in New York."
(From pp. 34-35 of "Mysteries of the Jesus Prayer: Experiencing the Presence of God and a Pilgrimage to the Heart of an Ancient Spirituality" by Norris Chumley).
There is no magic pill which will get us to experience interior silence. Ancient spiritual disciplines, such as lectio divina and praying the Jesus Prayer, are helpful practices - but our efforts, on their own, will not attain interior silence. The kind of silence that helps us to become aware of God's presence around us is a gift - a gift we can ask for through prayer, and when it is received, we cannot take credit for it, but only give thanks.