Looking at the bar below the health and the food, I'm guessing that you can level up in the new adventure mode. And the experience orb that they discovered in another picture fills up the bar. Also, without eating food, it would slowly damage you like staying underwater too long.
Notch on Twitter said that the level.class file now only takes one change to change the height of the map. He said that 128 is the max for now and that 256 took twice as much ram.
Looks like a food bar on the right and the armor bar underneath. Notch said he was going to add realistic mode, so hunger will probably only be in that mode. (and hardcore mode if they decide to do that finally)
Notch did post something on Twitter about an experience orb in Minecraft (He posted a super dark picture that was taken at night).