Today Verizon has started the rollout of the update to Android 5.0 Lollipop for Samsung Galaxy Note 3 units it's sold over the years. Previously, Lollipop was made available for the Note 3's successor, the Galaxy Note 4.
As always, the rollout will be staged, so you still may have a few days to wait before your particular phone notifies you about the update. If you're impatient, you can keep manually checking through Settings > About phone > Software updates and hope for the best.
After installing the new release, you'll be on software version LRX21V.N900VVRUEOB6. As you may know by now, Android 5.0 Lollipop brings with it the new Material Design, a new lock screen experience, floating action buttons everywhere, and a revamped recent apps menu. Additionally, Samsung has modified its TouchWiz UI overlay to fit in with Google's new design language, so the colors are bolder, the animations are fluid, and everything is brighter than before.