When your screen is off, battery-friendly notifications fade in and out, lighting only the pixels needed and showing notifications delivered since you last woke your screen. You can select which apps show notifications and limit content to control your privacy.
These notifications aren't displayed:
Check for notifications
If you haven’t seen activity for a while, to wake your phone, bump it.
View more and take action
From these notifications, you can:
Open the related app. Drag your finger up to the preview (then unlock if using a screen lock).
Dismiss a notification. Drag down to remove a notification.

Ignore for now. Drag your finger to the right or left edge of the screen to stop notifications from flashing until the next one is delivered.

Do any of the following:
To restart the notifications, turn Moto Display on
.