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 & 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
In Samsung Galaxy S4, it is called "Interruptions" under "Sound and notifications" menu.