What is the star icon in notification bar on Lollipop? Does anyone know what this icon means? The device is running Android 5.0 Lollipop.
This means that you only have priority notifications enabled. Pressing a volume button will allow you to select different notifications which show/make a sound.

There is a choice between no notifications, all notifications, and priority notifications, which can be changed by pressing a volume button. Going into Settings/Sound &amp; notification allows you to set which notifications have priority, such as only showing SMS and missed calls.

More help can be found here: https://support.google.com/nexus/answer/6111294