Notifications on the NextD Player are from the apps installed. The most common notifications are from the Google Play store and the 1 Mobile Market, especially when the device is just powered on, since the app stores typically update the installed apps automatically at this time.
To turn off the notifications in Google Play, 1 Mobile Market, or other apps that the users installed, simply launch the app that creates notifications then go into the "Settings" within that app to turn off the notifications.