What is the star icon in notification bar on 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