The roll in the front can help with placement so that the pad doesn't slide back. I think the rolls in the back are just for looks, but could also keep the pad from shifting under your saddle I guess (I've never had that problem though). Sometimes the ones with rear rolls are too narrow for dressage saddles, so make sure you know the measurment across your cantle and the measurement inbetween the rolls at the back of the pad before buying anything. If you're putting the pad under a square saddle pad, you don't want rolls in the back.
The other thing about the rolls in the back -- it limits the use of the half pad to putting it over a regular pad. I have two Horsedream pads without the back roll, and they can either go directly on the horse's back (as my ultra sensitive TB required), or over the cotton pad, as I do for my new girl right now until we get our fitted saddle.
"Reite dein Pferd vorwärts und richte es gerade.” Gustav Steinbrecht
Fron my experience it helps to keep the pad in place from front to back. I have never had mine slip but I had a friend that borrowed mine and she has a more active leg and it slipped left to right but moved with the saddle when the saddle slipped back because the girth was not tight enough. We tightened the girth added a nonslip pad and problem solved.
I have a sheepskin lined dressage pad with the rolls front and back, and two without, and do not have a problem with any of them slipping. These aren't half pads though...I really prefer the sheepskin next to horsie's back.