Or, alternatively, the ring / silent switch instantly accessible on the side of the device.

This is more useful than switching the side switch to 'silent mode', as this also suppresses the vibrate function.
The vibrator is often louder and more annoying than the quietest volume setting, particularly in low-noise environments. Turning the volume all the way down isn't the best solution either as it's easy to forget turing it back up again resulting in missed communications.
I wasn't aware of this setting as my DND options were obviously carried over from iOS6 I had no need to examine them until now. Thanks OP.

As the previous commenter posted - if you want silence, there is the silence switch.

This hint is still really useful for if you're using your iPad or iPhone as a presentation tool or in a group setting and don't want your Facebook messages popping up every few seconds. It's also great to for going "distraction free" if you are working on something.

This new mode makes it work more like Notification Center on OS X.