While this feature is enabled, the iPhone stops pushing most notifications. Emergency alerts, timers, and alarms can break through. You can optionally allow the phone to reply to incoming text messages with an explanation (and a way to break through if it’s really important).
Incoming calls are allowed to come through, but only when the iPhone is connected to a hands-free accessory like a headset or the car’s built-in audio system. Otherwise, the phone behaves like the normal Do Not Disturb—it will allow in the favorites you specify and repeated calls from the same person within three minutes.