The iPhone has a Silent switch on the side, but it doesn't make your phone ring and deliver alerts completely silent. The phone still vibrates, which is desirable for some but annoying for others. However, you can stop your phone from vibrating in Silent Mode by simply changing a few settings. Open the main page of the Settings app, open Sounds, then slide the first switch labeled "Vibrate" to the off position. Now, whenever your Silent switch is active, your phone will be completely silent, except for music and other sound from apps.