Yea, Do Not Disturb on iOS is actually a really nice feature that I wish would make it over to Android. The coles notes version:
1) it can silence all notifications between certain times (i.e.) at night, but still let the alarm ring
2) you can set it so "favourite" contacts who call will always make the phone ring even when DND is on.
3) you can set it so if someone calls twice within 3 minutes, the phone will actually ring the second time. This is good if someone really does need to get a hold of you. I personally always tell someone that if it is that important, call me twice. If you're calling twice in a row, generally that's a good indication that something is up, and I'll almost always answer the second time, even if I'm busy.
As someone who has a family member who is dealing with a significant health problem I have to keep my phone on with all sounds at full so I make sure if the phone rings in the middle of the night I hear it. The downside of this is that every so often an email notification will wake me up.
Now, I know I could set all other notifications to vibrate only but I don't want to have to do that every night and/or have everything but phone calls as vibrate only all the time. Do Not Disturb as it exists on the iPhone is a fantastic feature and needs to find its way to our side of the aisle.