While not playing media, the volume buttons control ringer volume. If you turn the volume all the way down and then press the volume button one more time it enabled Do Not Disturb. When you press the volume button again at any time, the volume indicator drops down from the top to show it is in Do Not Disturb. You can cancel Do Not Disturb by pressing the volume up button one more time or pressing the "Turn Off Now" link in the menu that shows the Do Not Disturb setting.

You can also Settings > Sound > Do not Disturb where you can change automatic settings, allow priority notifications which break through, etc.