What do the orange bars mean?
I believe that the orange part of the HP bar has something to do with recovering health. Details of this I can't really say, but based on how it reacts in battle, it's still safe to assume that it's tied to your HP in some form.
Notice Prompto's (プロンプト) HP in this small segment. This GIF was taken from the recent Jump Festa trailer and is all part of one scene. As you can see, the orange bar and the white bar are one in the same, as the orange section pulses white, indicating that it is connected with the HP bar. HOWEVER, it's not part of the current HP, as you can see Prompto goes from 686 HP and recovers to 714 at the end of the GIF, and you can see his white bar slowly crawl up.
What could this mean? Well, it's possible that it's health that can be recoverable during battle. We have only just been introduced to these orange bars since the Jump Festa trailer, so there's nothing to base this off of. However, given that they flash white, it must have something to do with the HP.
Another thing to notice is the orange diamond roughly beneath the HP value that looks similar to the points on each end of the HP bar as well. It's better exposed when a party member's health drops below this point; a critical state of health.
There's also a point where Prompto's entire bar goes red as well as the HP value itself, but I'm not sure what this means... The clip doesn't show anything that would indicate what causes this, so it's hard to say.
We'll have to wait until Tabata tells us what it is!