To be honest, i don't think it does. I've looked on numerous campaigns now, and i've got units in my recent campaign with 3 chevrons of experience, and their stats are absolutely identical to those of units with only 1 experience point, and they don't seem to perform any better at all...

Maybe the bonuses don't show on the stats screen and it may be that i'm just not noticing the difference in battle even though it's there, i don't know, but right now it seems to me that experience is broken.