I'm not certain but I believe that the 2nd option is for when you have multiple notifications; for example, on the lock screen. Usually, IIRC, the lock screen only shows two(?) notifications, which are usually the first two apps that have a notification. The 3rd and subsequent notifications do not show until the first two have been dismissed. I think that setting an app as Priority will jump that app's notification to the top slot.
In the pulldown notification shade, it can display more than two but depending on the app, the first slots can be taken up by long notifications (such as emails where more than the usual few lines are displayed), or some users have the volume controls and brightness controls up top, leaving little room for other notifications. Priority apps would show higher in the notification shade than it normally would if it was a later notification than the non-priority apps that may be in front of it.
There is some confusion with the word 'Priority' as it is also used as a 4th profile mode in Lollipop (sound, vibrate, silent and now priority). I admittedly may be mistaken but that is how I understand those.
All that said, if Priority really does refer to Priority profile mode (the yellow star mode), it may mean that notifications that normally do not display while in that mode now will if you have that app set to do so. I do not use Priority mode, so I am not sure -- hopefully someone else can chime in and confirm/deny. The reasons I don't use Priority mode are mainly because I've gotten by without it just fine; and also if I want the sound on, I set it to Sounds -- and if i don't, I set it to Silent.