The bar represents your progress towards the next unlock in that weapon group. The more you use a certain weapon class, vehicle, etc, the more you points you will earn toward an additional unlock in that category. You can see a more detailed view of this progression in your battlelog profile:
Sometimes the game will "forget" where certain points came from, and award them under additional points.
For example, I just received 2820 additional points BUT my jet score said that I'd scored 0 that round, but I'd actually scored the exact amount that I received in my additional points. It only forgot for the after round tally, as when I checked my vehicle tab, it remembered my actual amount of jet experience (I'd levelled up).
So it seems the varying amounts may be due to for instance, it not remembering that you got a particular ribbon, or a particular service medal.
Here's a video explaining what I mean. It's pretty bad quality, but as you can see, my jet score shows up as 0 when it's tallying points, and I gain 2820 "additional points". Then later when I switch to my vehicles tab, jets has +2820 experience.
Also, as of Back to Karkand (and I'm assuming future expansions will do this too) any assignments you complete will award you 5000 "Additional Points".
Additionally, any XP earned during a double XP weekend will earn you the same amount of XP extra under Additional Points.
Best Answer
They're an easter egg put in the game due to a meme that spread around the internet originating on 4chan because of a lack of dinosaurs in Call of Duty: Modern Warfare 2.
Basically when Battlefield 3 was announced, everyone was asking if there'd be a dinosaur mode.
Since they weren't actually putting a dinosaur mode in (or maybe they will in the future :P) they left lots of dinosaur related easter eggs around, one of them being the dinosaurs on Wake Island, another being the Dinosaur Dogtags and a third being this wallpaper that they circulated: