When you flip the ring/silent switch on your iPhone, it goes quiet while it's locked/asleep—mostly. But unless Do Not Disturb is turned on, your iPhone will still buzz the hum of its internal vibration motor when alerts that would otherwise ring out arrive.
But there's a fix. You can make your silenced iPhone be truly silent with a single flick of a virtual switch. Head over to Settings, and tap on Sounds. Switch Vibrate on Silent to off, and your phone will be both sound and vibration free when you slide the ring/silent switch to the quieter position.
Mac OS X Hints