When each piece of chicken is a different size, they will cook at an uneven rate. If you don't pound them out, some breasts will cook faster than others, leaving the thinner breasts dried out, while the thicker ones can be undercooked. Pounding also tenderizes the meat, making the cooked result more tender.
Why does pounding chicken tenderize it?
Goal #4: Pounding = Tenderizing
Pounding the meat can break this bundle apart, or at the very least, weaken its hold, allowing those muscle fibers to separate. Essentially, pounding meat is like pre-chewing it for you so that your mouth has less work to do when the chicken finally gets there.
What is the point of pounding meat?
Tenderizing meat with the mallet softens the fibers, making the meat easier to chew and to digest. It is useful when preparing particularly tough cuts of steak, and works well when broiling or frying the meat.