The Ambient Display is Google's way to add the Moto Display feature to the Nexus 6. If Ambient Display is enabled, it automatically turns on the screen (in black and white) as soon as a new notification arrives or you just hold your device and pick it up. To disable Ambient Display on Nexus 6, do as follows:
1. Go to the settings (The simplest way is to drag down the notification bar and tap the Settings icon)
2. Under the Device settings, tap to open the Display settings
3. Toggle the Ambient Display button to enable or disable the feature
** Note that the Ambient Display feature lets you interact with new notifications as soon as they arrive. So, to prevent any accidental actions, it is recommended to use a secure locking method (PIN, password, pattern...).