We've got a new baby. Sleep is a precious commodity right now. The last thing I want if I manage to sneak in a 30 minute nap is for someone to text, email, phone, or otherwise do anything to get between me and catching the fast train to sleepsville.
Do Not Disturb simply doesn't let any notifications, texts, phone calls, Game Center notifications or Twitter replies through. Short of an emergency (we'll get to that), your phone is dead to you so you can be dead to the world.
There's a quick On/Off toggle you can do to enable Do Not Disturb right away.
This effectively shuts the iPhone off to outside noises. One key point is that if you're using your iPhone (i.e. it's on and you're just checking Twitter one more time. Just one more time.) it will still vibrate and make noises as normal. I guess it assumes since you're using the iPhone you're ok with being disturbed.
But if you lock your iPhone and set it down/put it in your pocket, you'll be free from iPhone related disturbances.
Let's say you're taking your nap and one of your kids gets a call from the school that they got really muddy and you need to bring some pants - hypothetically speaking of course - Do Not Disturb's Allow Calls From option is where you want to look.
In Mail/Contacts in iOS 6 you can set certain people as Favorites. (You don't have to tell them - don't worry!) Then if those people are calling you it will allow them to get through the Do Not Disturb zone of sleep protection™.
Similarly you can set up groups of contacts in your Address Book and then check those off as being allowed through. This way you can have your school's phone number and important family/friends who you do want to allow to get ahold of you even if you're deep in sleep.
The last feature that you can turn on is Repeated Calls:
If enabled a second call from someone within a 3 minute time window will be allowed through. Like, for example, if the school really needs you to bring clean pants for your muddy kid.