Apps running on the Android, iPhone, and other iOS devices can be configured to send notification information to the Pebble's screen. The new version of the PebbleOS, v1.14, gives Pebble users a "Do Not Disturb" option, which blocks the watch from receiving any notifications for a set period of time.
Users will also have more control over which notifications are displayed and are able to choose to switch notifications on or off, or to only receive notifications about phone calls. These options are available via a dedicated menu in the phone settings.
Read more of "Pebble smartwatch update introduces 'Do Not Disturb' option" at ZDNet.